#I LOVE MATHS
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judith1122sblog · 2 months ago
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😍❤️
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facts-and-memes · 3 months ago
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I am definitely sure he never said that 😂
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shubhadeep385 · 2 months ago
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Face shading, seems time ⏰ consuming, but yields great results 🎇!!!
Art Credit : @shubhadeep385
Photo credit : @shubhadeep385
Dedicated to : Er. Ashok Kumar sir(our Maths teacher)
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claires-audience · 22 days ago
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The sheer number of math-question memes like, “My sister was twice my age when I was 5, so how old will she be when I’m 45?” proves two things:
1) we’re collectively terrible at math, and
2) this probably millennial-era joke has somehow achieved eternal life.Its unfazed by logic, surviving every generation.
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matias-2003 · 2 months ago
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The divisibility rules of every number from 1 to 100 with alternate methods for the numbers that end in 1, 3, 7 or 9
1: Every number is a multiple of 1
2: The number ends in 0, 2, 4, 6 or 8
3: The sum of the digits is a multiple of 3
4: The last 2 digits are a multiple of 4
The 10s digit is even and the last digit is 0, 4 or 8
The 10s digit is odd and the last digit is 2 or 6
5: The number ends in 0 or 5
6: The number is a multiple of 2 and 3 at the same time
7: The difference between twice the last digit and the rest of the number is a multiple of 7
8: The last 3 digits are a multiple of 8
The 100s digit is even and the last 2 digits are a multiple of 8
The 100s digit is odd and the last 2 digits are 4 times an odd number
9: The sum of the digits is a multiple of 9
10: The number ends in 0
11: The difference between the last digit and the rest of the number is a multiple of 11
12: The number is a multiple of 3 and 4 at the same time
13: The sum of 4 times the last digit and the rest of the number is a multiple of 13
14: The number is a multiple of 2 and 7 at the same time
15: The number is a multiple of 3 and 5 at the same time
16: The last 4 digits are a multiple of 16
The 1,000s digit is even and the last 3 digits are a multiple of 16
The 1,000s digit is odd and the last 3 digits are 8 times an odd number
17: The difference between 5 times the last digit and the rest of the number is a multiple of 17
18: The number is a multiple of 2 and 9 at the same time
19: The sum of twice the last digit and the rest of the number is a multiple of 19
20: The number ends in 00, 20, 40, 60 or 80
21: The difference between twice the last digit and the rest of the number is a multiple of 21
22: The number is a multiple of 2 and 11 at the same time
23: The sum of 7 times the last digit and the rest of the number is a multiple of 23
24: The number is a multiple of 3 and 8 at the same time
25: The number ends in 00, 25, 50 or 75
26: The number is a multiple of 2 and 13 at the same time
27: The difference between 8 times the last digit and the rest of the number is a multiple of 27
28: The number is a multiple of 4 and 7 at the same time
29: The sum of thrice the last digit and the rest of the number is a multiple of 29
30: The number is a multiple of 3 and 10 at the same time
31: The difference between thrice the last digit and the rest of the number is a multiple of 31
32: The last 5 digits are a multiple of 32
The 10,000s digit is even and the last 4 digits are a multiple of 32
The 10,000s digit is odd and the last 4 digits are 16 times an odd number
33: The sum of 10 times the last digit and the rest of the number is a multiple of 33
34: The number is a multiple of 2 and 17 at the same time
35: The number is a multiple of 5 and 7 at the same time
36: The number is a multiple of 4 and 9 at the same time
37: The difference between 11 times the last digit and the rest of the number is a multiple of 37
38: The number is a multiple of 2 and 19 at the same time
39: The sum of 4 times the last digit and the rest of the number is a multiple of 39
40: The last 3 digits are a multiple of 40
The 100s digit is even and the last 2 digits are 00, 40 or 80
The 100s digit is odd and the last 2 digits are 20 or 60
41: The difference between 4 times the last digit and the rest of the number is a multiple of 41
42: The number is a multiple of 2 and 21 at the same time
43: The sum of 13 times the last digit and the rest of the number is a multiple of 43
44: The number is a multiple of 4 and 11 at the same time
45: The number is a multiple of 5 and 9 at the same time
46: The number is a multiple of 2 and 23 at the same time
47: The difference between 14 times the last digit and the rest of the number is a multiple of 47
48: The number is a multiple of 3 and 16 at the same time
49: The sum of 5 times the last digit and the rest of the number is a multiple of 49
50: The number ends in 00 or 50
51: The difference between 5 times the last digit and the rest of the number is a multiple of 51
52: The number is a multiple of 4 and 13 at the same time
53: The sum of 16 times the last digit and the rest of the number is a multiple of 53
54: The number is a multiple of 2 and 27 at the same time
55: The number is a multiple of 5 and 11 at the same time
56: The number is a multiple of 7 and 8 at the same time
57: The difference between 17 times the last digit and the rest of the number is a multiple of 57
58: The number is a multiple of 2 and 29 at the same time
59: The sum of 6 times the last digit and the rest of the number is a multiple of 59
60: The number is a multiple of 3 and 20 at the same time
61: The difference between 6 times the last digit and the rest of the number is a multiple of 61
62: The number is a multiple of 2 and 31 at the same time
63: The sum of 19 times the last digit and the rest of the number is a multiple of 63
64: The last 6 digits are a multiple of 64
The 100,000s digit is even and the last 5 digits are a multiple of 64
The 100,000s digit is odd and the last 5 digits are 32 times an odd number
65: The number is a multiple of 5 and 13 at the same time
66: The number is a multiple of 2 and 33 at the same time
67: The difference between 20 times the last digit and the rest of the number is a multiple of 67
68: The number is a multiple of 4 and 17 at the same time
69: The sum of 7 times the last digit and the rest of the number is a multiple of 69
70: The number is a multiple of 7 and 10 at the same time
71: The difference between 7 times the last digit and the rest of the number is a multiple of 71
72: The number is a multiple of 8 and 9 at the same time
73: The sum of 22 times the last digit and the rest of the number is a multiple of 73
74: The number is a multiple of 2 and 37 at the same time
75: The number is a multiple of 3 and 25 at the same time
76: The number is a multiple of 4 and 19 at the same time
77: The difference between 23 times the last digit and the rest of the number is a multiple of 77
78: The number is a multiple of 2 and 39 at the same time
79: The sum of 8 times the last digit and the rest of the number is a multiple of 79
80: The last 4 digits are a multiple of 80
The 1,000s digit is even and the last 3 digits are a multiple of 80
The 1,000s digit is odd and the last 3 digits are 40 times an odd number
81: The difference between 8 times the last digit and the rest of the number is a multiple of 81
82: The number is a multiple of 2 and 41 at the same time
83: The sum of 25 times the last digit and the rest of the number is a multiple of 83
84: The number is a multiple of 4 and 21 at the same time
85: The number is a multiple of 5 and 17 at the same time
86: The number is a multiple of 2 and 43 at the same time
87: The difference between 26 times the last digit and the rest of the number is a multiple of 87
88: The number is a multiple of 8 and 11 at the same time
89: The sum of 9 times the last digit and the rest of the number is a multiple of 89
90: The number is a multiple of 9 and 10 at the same time
91: The difference between 9 times the last digit and the rest of the number is a multiple of 91
92: The number is a multiple of 4 and 23 at the same time
93: The sum of 28 times the last digit and the rest of the number is a multiple of 93
94: The number is a multiple of 2 and 47 at the same time
95: The number is a multiple of 5 and 19 at the same time
96: The number is a multiple of 3 and 32 at the same time
97: The difference between 29 times the last digit and the rest of the number is a multiple of 97
98: The number is a multiple of 2 and 49 at the same time
99: The sum of 10 times the last digit and the rest of the number is a multiple of 99
100: The number ends in 00
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thecrazyphantom · 3 months ago
Note
(x^2 + y^2 + a x)^2 = a^2(x^2 + y^2)
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I'm not sure if I did this right.
Also, what am I solving for?
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communistmishka · 2 months ago
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The week off is over, and I'm finally back to studying. Currently reading: "Introduction to Mathematical Philosophy" by Bertrand Russell. I can already tell it's gonna be quite a ride
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mystupidarse · 3 months ago
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i wuv math <3
it was so simple after all...
i just had to take learning as a hobby! <3
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gayhorrorsans · 7 days ago
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So I'm also a nerd too
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Got the right answer tho 😏
so yknow... if u need help at all... my asks are.. open.
I'm going through a blank space in writing cause I sorta cba and I'm struggling for inspo. Sooo if you're stuck on a topic lmk!
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literallycogsworth · 8 months ago
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‘How was maths?’
The maths in question:
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(I do extracurricular maths for anyone that’s wondering 😭)
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itsgerges · 2 months ago
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The Gravitational Waves Reflection Analysis (Revised)
or
or
or
Paper 1st hypothesis
The gravitational waves are produced by the planet motion energy and Not by the gravitational field- Moreover- the sun doesn't produce a gravitational field -Shortly- the planet motion produces energy (1/2 mv^2) and this energy is stored in the space as moving waves – these are the gravitational waves- also the gravitational waves are reflected in the solar system and the wave reflection causes to square the wave velocity
Paper 2nd hypothesis
The Sun Is Not Doing Nuclear Fusion To Produce Its Rays– Because
This Is Extraordinary: Gravity Can Create Light, All on Its Own
https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsnHYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"&HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"cvid=620db4352aa943e2b454919a7b724604HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"&HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"ei=83
This new article tells the gravitational waves can move by speed of light and can produce a light beam- I claim the sun rays are produced based on this method by the gravitational waves motions and not by the sun nuclear fusion process- also –No star rays is produced by the nuclear fusion process but all rays are created by the gravitational waves motions energies as the article states.  
Paper 3rd  hypothesis
The planets Motions use different rates of time – the rate of time depends on the velocities rate – example- Mercury velocity = 1.6 the Earth velocity because of that (One Second Of Mercury Clock  = 1.6 Seconds Of The Earth Clock)
Paper 4th  hypothesis
Neptune motion caused to create relativistic effects in the solar system because
This Is Extraordinary: Gravity Can Create Light, All on Its Own
https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsnHYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"&HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"cvid=620db4352aa943e2b454919a7b724604HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"&HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"ei=83
the new article tells the gravitational waves can move by speed of light-
and the gravitational waves move by speed of light but Neptune caused to decrease the wave speed by 1% and by that the speed be equal 99% of speed of light (=297000 km/s) which caused to created relativistic effects in the solar system- also- Neptune caused to create two wave reflections in the outer planets which one reflection only was enough- means- if Neptune is removed from the solar system the wave reflections in the outer planets will be one reflection only and not two reflections 
Paper Main Argument
The Physicist Vision Contradicts The Nature System 
I study the solar system Geometry since long years- and- I have found the physicist and astronomer can't understand the solar system designer vision– in fact their vision contradict the designer vision- let's prove that in following  
The Physicist Vision
The physicist supposes that there's (a unit of building)- by that- the physicist sees the mass (for example) as wall and this wall is consisted of bricks (small similar units) and for that the physicist searched for this (unit) because it's the (unit) by which the wall is building (the mass is building)– this is the physicist thinking direction- he believed there's a small unit by which the great building is built
For that the physicist searched and found the particle and then the particle is divided into Molecules then the Molecule is divided into atoms and the atom is divided into nucleus and electron moves around and the nucleus is divided into proton and Neutron- and the proton is divided into quarks …etc
The physicist searches for the building unit- the unit by which the building is built – or the unit by which the mass is built – for that the physicist divides (any thing) to see its contents till reach to the unit which can be used as the building unit. 
The Designer Vision
The designer aims to create integration- as the marriage – male and female- the relationship will cause to give birth for a child
INTEGRATION this is the word inside the designer Mind
No building unit- the marriage answers- because in marriage both (male and female) are required and no one of them better than the other – both work together and give equal effects on the same one process and give together one result- I explain the idea by the marriage because it's easy to understand- I want to put the word (Integration) as the basic concept in the designer mind.
And
I want to explain how the physicist causes fatal error for the research method
While the physicist divides the elements one after one (from matter to particle to molecule to atom to proton to quarks …etc) this division from out into inner till reach to very small unit which he considered the building unit – that causes to destroy the geometrical design of the integration process
Let's return to the marriage- the marriage requires two players (male and female)- they have different bodies and the process give birth for children- Suppose we remove one player what would happen? (where can we find a woman pregnant by herself?)
I want to say- the division from (matter to particle to molecule to atom to proton to quarks …etc) destroys the general geometrical design which uses the integration process- let's give other examples
Example No. (1)   
Einstein told us (He can't find slightest meaning for the word SPACE) by that he can't define (what's the space) and also he found the space has no mechanical features because no definition causes these features – this is the physicist vision - Let's see the designer vision
Planet moves and its motion produces energy (1/2 mv^2) and where's the energy? the planet can't store its motion energy inside its body because this energy would raise the planet temperature and no planet temperature is raised by its motion- so- where's the planet motion energy? logically we suppose that- the energy is stored in the space in waves form- means- the planet moves and its motion energy creates waves in the space (as the fish swims in the sea and its motion creates waves in the sea water) similar to that the planet motion produces energy and this energy creates waves in the space- by that we can define the space and conclude the space nature and features- simply we conclude the space has mechanical features because the energy is stored in the space as moving waves- the gravitational waves prove the space has motion- why we can solve the question which Einstein couldn't solve? Because he supposed the planet is independent from the space- the integration concept is not known by him
Notice
The waves are produced by the planet motion energy are the gravitational waves, the paper first hypothesis proves these waves are produced by the planets motions energies and not by the gravitational field also the hypothesis proves the Sun doesn't produce a gravitational field.   
More examples are provided after the hypotheses explanations 
PAPER FIRST HYPOTHESIS
Paper first hypothesis
The gravitational waves are produced by the planets motions energies and not by the gravitational field (Moreover the sun is not producing a gravitational field) and
The gravitational waves are reflected three times in the solar system (from Pluto and Neptune to Saturn) and (From Uranus to Jupiter) and (from Venus to Mars) –
The gravitational waves reflection causes changes in the planets data- and these changes are repeated with each reflection- means- these changes are found by rules because it's repeated with each reflection clearly- that shows the planets use similar behaviors to create their data which proves one reason causes to create all this data
Also- the wave energy reflection causes to square the wave velocity – the velocity square is the most important feature of the energy reflection because it enables the waves to move by speed of light- that explains how the gravitational waves can move by speed of light in the solar system- the motion by speed of light is produced only by the wave energy reflection (and without the reflection this motion can't be done)     
Paper 1st hypothesis (The objective of the hypothesis)
I prove that the gravitational waves are produced by the planets motions energies and these waves are reflected in the solar system three time and the reflection of the wave energy causes to square the wave velocity (the velocity squaring is the important feature I prove in the paper because the light beam is reflected but its speed is NOT squared and that means the wave velocity squaring is feature of the space) and it's very important to prove the wave velocity is squared by the reflection because this process enables the waves to move by speed of light and that explains how the gravitational waves can move by speed of light – as this new article states
This Is Extraordinary: Gravity Can Create Light, All on Its Own
https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsnHYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"&HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"cvid=620db4352aa943e2b454919a7b724604HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"&HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"ei=83
The article tells, the gravitational waves can move by speed of light and can produce a light beam- here I explain how the gravitational waves can move by speed of light (please note the article still believes the gravitational waves are produced by the gravitational field – I refuse this idea – the gravitational waves are produced by the planets motions energies but the article states that the gravitational waves can move by speed of light and can produce a light beam and I accept this idea and I explain and prove how the gravitational waves can move by speed of light) 
Paper 1st hypothesis Proof (The Proving Method)
I compare between the planets data in the three reflections of the wave- I put the planets data in comparison to each other for each reflection to prove the planets use similar behaviors to define their data and this similar behavior proves one force (or one reason) is found behind- and this one reason is the wave energy reflection which causes to create all this data –
The wave energy reflection effect on the solar system design (A Summary)
The reflections cause defined changes in the planets data – and
The most important change is (the wave velocity square) – and this velocity squaring is very important because it enable the gravitational waves to move by speed of light – the motion by speed of light is very effective on the solar system design because it defines the planets distribution between the sun and Pluto– this fact is explained in point no. (**) 
Paper 1st hypothesis Explanation and Proof Discussion
Paper 1st hypothesis Explanation and Proof Discussion
The explanation is discussed in two parts
1ST PART
I- Preface
II- The Comparison
III- The explanation of the wave energy reflection effect on the solar system design
2nd PART
The Gravitational Waves Reflection Detailed Discussion
(Paper 1st hypothesis Explanation) 1ST PART
I- Preface
(1)
Planet Motion Energy Analysis
Planet motion produces energy (1/2 mv^2), where's Planet motion energy? the planet can NOT store its motion energy inside its body because it would raise its temperature and No planet temperature is raised by its motion- logically- the planet motion energy is stored in the space in waves form- means- Planet motion energy creates waves in the space- the planet motion in the space is similar to a fish swimming in the sea- as the fish swimming creates waves in the water the planet motion energy creates waves in the space- let's see this picture clearly- the fish swims because it hits the water by its body and that creates waves in the water- we conclude, the water waves move by a velocity equal the fish velocity because of the reaction force- similar to that- Planet moves in the space and its motion energy creates waves in the space and these waves move by velocity equal the planet velocity- for example- Mercury (47.4 km/s) moves and its motion energy creates waves in the space and these waves move by equal velocity (47.4 km/s)- based on this idea- All planets move and their motions energies create waves in the space where each wave moves by velocity equal its planet velocity
(2)
These Waves Are The Gravitational Waves (My Hypothesis)
Mans- the waves are produced by the planets motions energies- these waves are the gravitational waves- it's my paper 1st hypothesis- the gravitational waves are not produced by the gravitational field (moreover the sun doesn't produce a gravitational field) instead the gravitational waves are produced by the planets motions energies 
AND
The planets revolve around the sun in the same one direction and for that their motions energies create waves in the space and these waves move perpendicular on the revolution direction (Toward Pluto orbit)
AND 
In Pluto orbit these waves are unified together into one unified wave- this wave moves by a velocity = 205.8 km/s why? The 9 planets velocities total=176 km/s but I add the Earth moon velocity (29.8 km/s) that makes the total to be 205.8 km/s – I add the moon velocity because the energy is stored finally in the moon orbit-
Note- The moon and the Earth revolve around the sun together for that the moon velocity is considered equal the Earth velocity relative to (the sun) –
The 1st Conclusion
The Planet Motion Energy Creates Waves In The Space
Means - The Space Must Have Moving Waves  -
Now -the scientists had discovered waves in the space- And- they considered these waves are produced by The Sun Gravitational Field – BUT Why?
The planet motion energy analysis proves the waves must be produced by the planets motions energies- Now let's refute the sun gravitational field theory- the refutation gives support for the conclusion – the gravitational waves are produced by the planets motions energies and NOT by the gravitational field because there's NO Gravitational field.
(3)
The Refutation Of The Sun Gravitational Field
The Sun Doesn't Produce A Gravitational Field Nor Has Massive Gravity – let's prove that in following
(i)
The sun rotation period is (25.4 days– at equator) and (34.4 days – at pole) that shows the sun has no massive gravity nor even ordinary gravity equal any planet gravity otherwise the sun would rotate around its axis in one period of time- 
(ii)
No Planet Moves By The Sun Gravity–Newton is wrong- because- the planet moves by the force caused its creation- means- the planet creation and motion is done by one force only- because- if two forces have effects on the same one planet this planet would be broken- now- suppose the planet is created (by any force) and the sun gravity attracted this planet and forced it to revolve around the sun by the sun mass massive gravity (as Newton imagined) that would force the planet to move against its inner structure and will cause this planet to be broken- this is similar to a human is forced to walk on his hands in place of his legs and when this human refuses to do that (they told him we can force you by our power) for that this human walk on his hands forcedly and later this human is dead by this motion- shortly- the planet is NOT broken by its motion because the planet creation force is the force causes this planet motion- it's one force caused the planet creation and motion-
Newton mistake is that he didn't know how the planet is created and by that he didn't realize that planet creation and motion are done together by the same one source- simply- the sun didn't cause to create any planet and for that the sun doesn't cause any planet to move- this analysis shows logical base but left us with puzzles to know (by what rule the planet moves?) and (Why is the sun found in the solar system if it doesn't cause the planets motions?) these questions are answered in the paper abstract and discussions.  
(iii)
The mass gravity force can NOT cause any motion- again Newton is wrong- the mass gravity creates a bond between two masses- (the Earth and the moon are bond by the mass gravity)- by that they are similar to a lorry and its trailer – if the lorry moves the trailer will move with the lorry- but the mass gravity can NOT cause any motion- why? suppose the moon moves by the Erath gravity force- the moon moves and produces energy (1/2mv^2) and we have to ask from what source this energy will be provided?- from the mass itself- means if the Earth causes the moon to move the Earth and the moon masses should be decreased by the motion energy- this is a wrong definition for the mass gravity- the mass gravity creates a bond between two masses (The Earth and the moon) if some outer force causes the Earth to move the moon will move with the Earth and in this case the outer force will provide the motion energy for the Earth and the moon-
(iv)
The planets order contradicts Newton gravitation equation- where- the gravitation equation tells (greater mass necessitates shorter distance)- clearly- Jupiter the greatest mass is not the most near planet to the sun- means- the planets order contradicts the equation- when we asked the physicist told us this problem is done by (the initial conditions)- all these are nonsense clearly- planet orbital distance does NOT depend on the sun mass nor on the planet mass- planet orbital distance depends on the neighbor planet orbital distance – my equation proves this fact- let's see it
Planet orbital distance equation (my 1st equation)
d^2= 4do (d-do) where d= planet orbital distance and do= its neighbor distance
Example (1) Venus orbital distance (108.2)^2 = 4 x 57.9 x (50.3)                              
d= 108.2 million km = Venus Orbital Distance
d0= 57.9 million km  = Mercury Orbital Distance
50.3million km=The Distance Between Venus And Mercury  Venus Depends On Mercury
Example (2) Saturn orbital distance (1433)^2= 4 x 778.6 x 655
d= 1433 million km    = Saturn Orbital Distance
d0= 778.6 million km  = Jupiter Orbital Distance
655million km=The Distance Between Saturn And Jupiter Saturn Depends On Jupiter
All planets orbital distances are defined based on their previous neighbor planets orbital distances- the equation is correct perfectly and all planets orbital distances are defined by it- my paper tests and discusses this equation
Shortly- planet mass has no any effect on this planet orbital distance definition.
Notice
Planet orbital distance definition depends on its neighbor orbital distance this fact is proved by many other different methods my equation is one method only of them, all these methods don't use any planet mass- all planets orbits are defined based on their neighbor orbits- (Please note- Newton gravitation equation is wrong- I don't critic it by many critics to short the discussion- but- the fact is that- the light beam created all planets orbits before any planet creation- the light created each planet orbit depends on its neighbor orbit- I prove this fact in the paper discussion- logically this fact kills the gravitation equation because the orbit is created before the planet creation)  
Notice -Newton is so far from the truth- let's give one more example- Newton told us planet moves by the sun mass gravity- the fact is that- the Sun itself is created by the planets motions energies- that's why Newton ideas are not interesting for discussion because his ideas are imaginary have no part of truth-
(v)
Also-Newton told-planet motion depends on its mass- means-planet velocity depends on its mass- this also is imaginary idea- I define planet velocity in the paper abstract- planet velocity is defined by many rules all of them don't use any planet mass- at all Planet mass has no rule in this planet velocity definition.
The 2nd Conclusion
The Gravitational Waves Are Produced By The Planets Motions Energies And Not By The Sun Gravitational Field- Also-There's No Gravitational Field At All
(4)
The Wave Reflection Trajectory
Let's remember what we know till now
(a)
Planet motion produces energy (1/2 mv^2) and this energy creates waves in the space and each wave moves by its planet velocity- these waves move toward Pluto (perpendicular on the revolution direction) and in Pluto orbit these waves are unified into one unified wave moves by velocity = the planets velocities total = 205.8 km/s  
Means- while the planets revolve around the sun in their orbits by their velocities- there's one unified wave revolves around the sun moving by 205.8 km/s and this unified wave revolves around The Sun In Pluto Orbit-this unified wave is The Gravitational Wave  
Now- this unified wave is reflected from Pluto to Venus orbit- Means- the unified wave is reflected and sent from Pluto to Neptune to the next planets till reach Venus 
The unified wave is reflected three times in the solar system
(from Pluto and Neptune to Saturn) and
(from Uranus and Jupiter) and
(from Venus to Mars)
With each reflection of the wave defined changes are done for the planets data
But let's refer to the general design behind these three reflections in following
(b)
We remember this new article
This Is Extraordinary: Gravity Can Create Light, All on Its Own
https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsnHYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"&HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"cvid=620db4352aa943e2b454919a7b724604HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"&HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"ei=83
The article tells, the gravitational waves can move by speed of light and can produce a light beam-
My hypothesis tells (the reflection of energy causes to square the wave velocity)
Let's put the ideas beside one another to see the general design
The gravitational waves can move by speed of light AND can produce a light beam – How?? if the motion is done by speed of light (C=300000 km/s) how can this motion produce a light beam? Because the light beam is produced from the value (C^2 = squared speed of light) – here we see the energy reflection effect- the wave moves by speed of light and when this wave is reflected its velocity is squared and produced the value (C^2 = squared speed of light) from which the light beam is created-
Means
The machine needs one reflection to change the speed from (speed of light C=30000 km/s to the value C^2 =squared speed of light) and by that the light beam is created
Now – let's ask -
How can the wave moves by speed of light?
We remember- the one unified wave (the gravitational wave) moves in Pluto orbit with velocity 205.8 km/s – how can this gravitational wave moves by speed of light? 
By another reflection of energy – let's see that in following
300000 km/s = (205.8 km/s)^2 x 7.1
This equation tells
The unified wave (the gravitational wave) moves by 205.8 km/s and it's reflected, the waves reflection causes to square the velocities
(205.8 km/s)^2 = 42683 km/s
Means the gravitational wave after the reflection moves by a velocity 42683 km/s
BUT
If a particle moves by speed (=0.99 C=297000 km/s), this high velocity motion causes to create relativistic effects specially Lorentz length contraction effect with rate 7.1
Means- the distances should be contracted by the rate 7.1
BUT
The waves reflection causes to reflect the geometrical effects and by that the rate (7.1) will cause to increase the length in place of the length contraction- means- the distances will be increased with (7.1) as a result for Lorentz length contraction effect
The velocity 42683 km/s will be 42683 x 7.1 = 300000 km/s (Speed Of Light) 
That explains how the gravitational waves move by (205.8 k/s) can move by speed of light (C=300000 km/s)
Here we see clearly that
The machine needs one energy reflection only to accelerate the wave velocity from 205.8 km/s to move by speed of light (C=300000 km/s)
And
The machine needs one more reflection only to change the wave speed from the speed of light (C=300000 km/s) to (C^2 =squared speed of light) by which the light beam is created
Shortly -the machine needs only two reflections of energy to produce the light beam from the gravitational waves motions
Now – let's ask– Why Are There Three Reflections Of Energy In The Solar System? If The Machine Needs Just Two Reflections Why The Machine Uses Three Reflections? 
Because of Neptune negative effect on the solar system motion- Neptune caused to repeat the energy reflection and by that the solar system uses 2 reflections in the outer planets and one reflection in the inner planets- this result is done by Neptune negative effect on the solar system motion – as explained in details in the third hypothesis.   
(c)
Please note- the two reflections in the outer planets are done to produce a result of one reflection only and for that the two reflections are complementary one another as we will discuss- shortly- we can say there's one unified reflection of the wave in the outer planets and one single reflection of the wave in the inner planets because the two reflections in the outer planets are complementary each other and produce a result of one reflection only – spite of that- the planets data prove clearly there are three reflections in the solar system- means- while the wave reflections are three they do effect of two reflections only – as we will discuss in details in following
(5)
 The Wave Acceleration Process
Now we know the unified wave velocity is 205.8 km/s and this wave is accelerated to move by speed of light (C=300000 km/s) by one reflection and then this wave moves by speed of light is accelerated one more time to produce the value (C^2= squared speed of light)  by another reflection   
But where's this happened? In which planets orbits this is happened?
Shortly
The wave moves by 205.8 km/s in the orbits of Planets (Pluto – Neptune and Uranus) and
The wave velocity is accelerated to move by speed of light in Saturn orbit
Means- Starting from Saturn orbit the unified wave moves by speed of light – the wave speed is speed of light in all orbits from Saturn to Venus
And
Venus reflected the wave to Mars and that causes to accelerate the wave velocity from the speed of light (C=300000 km/s) to (C^2= squared speed of light)- in the moon orbit between Venus and Mars    
(6)
 Planet Definition 
(A)
The physics book defines the planet as (Planet is solid body created independently from the space and the other planets)–if so- how can the gravitational waves reflection have effects on the planets data??
My definition for the planet is
Planet is a geometrical point carried on the moving energy (or Planet is a geometrical point found on a light beam) – let's explain this definition in following
The matter and space both are created from the same one energy- means
The planets matters and their distances both are created from the same one energy- the matter and space move depending on the motion of this energy from which they are created-means- the matter isn't moving by the mass gravity – Newton is wrong- the matter moves by the motion of the energy from which the matter is created- 
Based on this idea
The space is similar to the sea of water- and the matter is similar to a whirlpool (vortex) is found on the sea page- the matter creates for itself a geometrical frame (a distinguished form from the space) and moves by a different velocity from the space motion- as the whirlpool (vortex) on the sea page- it's created by the sea water but it has a distinguish form from the sea waves and it moves by a different velocity from the sea waves- this explanation shows how the moving energy can effect on the matter creation data- for example- we have a whirlpool (vortex) its diameter is 2 meters how is this whirlpool created? and why does its diameter equal = 2 meters? The diameter is created as a result for the water motion velocity, pressure, amount and motion angle and many other features of (the moving water)- the moving water creates this whirlpool with diameter 2 meters and as long as the water motion is not changed this diameter will not be changed also-   
Let's give another example
The energy motion is similar to the blood motion in a creature body- suppose- we examine now a liver of human - the blood motion causes this liver to work perfectly but if the blood motion is changed that would cause changes for the liver cells and job – suppose the blood have some poison the liver will be dead- suppose the pressure is raised- I want to say- the liver is a piece of body (matter) but it depends on the blood motion and this blood motion defines this liver dimensions and data- 
Shortly–the matter is similar to a muscle in a creature- the muscle may be so strong as a rock but it depends on the blood motion (similar to that the matter is found depending on the motion of energy from which this matter is created)
That explains how the gravitational waves reflection have effects on the planets data- still the planet is a solid body and the wave is a wave- the wave can be reflected but the solid body can NOT be reflected spite of that the planets data is reflected one another because the reflected waves have effects on the moving energy by which this planet (solid body) is created-
(B)
We should see the depth of this new definition-
The definition tells us
The matter (planet) is created by energy and the matter moves with this energy- means- this energy is the mother of this matter- this energy created the matter and caused this matter motion-BUT- this definition tells- the matter motion is defined before the matter creation- means- Planet motion is defined before this planet creation- How can that be possible? Because –
The energy is found alone in motion (the sea water was in motion) and the energy created the matter and this matter dimensions and data is defined based on the energy motion features (as discussed before- the whirlpool "vortex" is created with diameter 2 meters and this diameter is defined by the water motion features "velocity- pressure- angle- amount …etc") by that the matter dimensions are defined by the mother energy motion features - AND after the matter creation, the matter moves with the mother energy- by that- the created matter moves the same motion based on which this matter dimensions and data is defined- that explains how the planet motion is defined before the planet creation-
This fact is proved by my planet diameter equation because it proves strongly that the planet diameter is created based on its velocity- means- the equation proves – for example – Neptune diameter is 49528 km because Neptune velocity is 5.4 km/s and Neptune velocity is defined before Neptune diameter- let's remember this equation
My Planet Diameter Equation (v1/v2)= (s/r)= I
v = Planet Velocity                                                         
r = Planet Diameter
s= Planet Rotation Periods Number In Its Orbital Period
I= Planet Orbital Inclination        (example, 1.8 degrees be produced as a rate 1.8)
v2, s, r and I are belonged to one planet and v1 is belonged to another planet
The planet (v1) is defined by test the minimum error 
Earth Equation uses Neptune velocity
Mars Equation uses Pluto velocity
Jupiter Equation uses the Earth moon velocity
Saturn Equation uses Mars velocity
Uranus Equation uses Neptune velocity (As Earth)
Neptune Equation uses Saturn velocity
Pluto Equation uses the Earth moon velocity (As Jupiter)
Example    
Neptune Equation (89143 /49528) = 9.7/ 5.4 =1.8                
89143          = Neptune rotation periods number in Neptune orbital period
49528 km     = Neptune diameter
9.7 km/s      = Saturn velocity
5.4 km/s      = Neptune velocity
59800 days  = Neptune orbital period (and Neptune rotation period =16.1 hours)
1.8 degrees = Neptune Orbital Inclination
The Equation Concept (A Summary)
Planet diameter should be a function in its orbital distance –otherwise- this planet would be broken by its motion- BUT- the designer can't create a function has only 2 variables (Planet diameter and its orbital distance)- because– If this planet changes its orbital distance its diameter would be broken also because the diameter is a direct function in the orbital distance without any other variables -As A Result  
The designer created the planet diameter as a function in this planet rotation period and the planet rotation period is created as a function in this planet velocity and the planet velocity is created as a function in this planet orbital distance- by that- the function Planet diameter and its orbital distance is created but also it contains many variables (rotation period, orbital period and velocity)- by that- if a Planet changes its orbital distance- this planet orbital period, and velocity and rotation period would be changed but its diameter will be saved-
(C)
The previous explanation helps us to see how the planet is created- also we remember Kepler rule (Planet Orbit Defines Its Velocity)  
The orbit is created at first and the orbit defines the motion velocity and the planet diameter is created based on this velocity –means- the space is created before the matter creation- Shortly- The planet orbit is created (from the mother energy) before this planet creation and the planet is created later (by this energy motion features) and the planet data is defined based on this motion features and the planet moves after Creation with this mother energy motion- and– in case any planet after creation changes its orbit the planet motion data be changed but its creation data is saved- we should note that the space must be created based on a geometrical design-means- the solar system space (all orbits) is designed based on one geometrical design before any planet creation
(D)
The planet is a geometrical point on the mother energy and moves with it –Or
The planet is a geometrical point on the same light beam and moves with it
That tells
The solar planets are geometrical points found on the same one light beam and move with this light beam motion
By that- the planets are similar to carriages in one train –and the light beam (the mother energy) is the engine of this train- the light moves and causes all planets motions  (as the sea water moves and causes all ships motions)
Here we conclude that the planets motions are similar to the chess board motions because it depends on geometrical rules in all details- that's why the analysis is so useful because it can show the geometrical design found by the planets motions integration.
(E)
The planet definition answers the question
If The Gravitational Waves Are Reflected Why This Reflection Have Effects On The Planets Data?
Because the waves reflection causes to define the energy motion direction and by that the planets data is changed and effected by the moving energy through these planets-
The effects on the planets data is very useful because it proves the reflection is a fact as we discussed later
(7)
 The Energy Distribution In The Solar System
Now we know
The unified wave (the gravitational wave) moves by 205.8 km/s in the orbits of Pluto, Neptune and Uranus and
The unified wave motion is accelerated to move by speed of light (C=300000 km/s) in all planets orbits Starting from Saturn to Venus
And Venus reflected the wave to Mars and by that the speed of light is squared to produce (C^2= squared speed of light) by which the light beam is created  
Can The Wave Different Speeds Have Effect On The Solar System Design? YES
The three planets (Pluto, Neptune and Uranus) have great areas because the wave velocity is 205.8 km/s means massive amounts of energy is stored in these orbits as waves move by 205.8 km/s-
But
Starting from Saturn orbit the wave moves by speed of light (C=300000 km/s) that doesn't need great areas because the energy is found in waves move by speed of light that explains why the planets orbits be small orbits (from Saturn to Venus) and even the inner planets have very small orbits because the energy is not stored in the inner planets orbits but the energy is used directly to produce the sun rays- that shows the planets distribution between the Sun and Pluto is related to the wave velocity changes
(8)
 Planet Motion Definition
Let's ask
This Is Extraordinary: Gravity Can Create Light, All on Its Own
https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsnHYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"&HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"cvid=620db4352aa943e2b454919a7b724604HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"&HYPERLINK "https://www.msn.com/en-us/news/technology/this-is-extraordinary-gravity-can-create-light-all-on-its-own/ar-AA19YL5d?ocid=hpmsn&cvid=620db4352aa943e2b454919a7b724604&ei=83"ei=83
The article tells, the gravitational waves can move by speed of light and can produce a light beam- now we ask- if the gravitational waves move by speed of light- why is it necessary the gravitational waves move by speed of light relative to the sun point of Space? Or let's ask this question by another method
Pluto velocity is 4.7 km/s relative to what? relative to the sun
All Motions In The Solar System Are Done Relative To The Sun – let's explain why
Let's remember how the sun point is created
We understand the space is similar to the sea of water and it's in continuous motion and NO stationary point can be found in it- the sun point of space should be a stationary point- for that the sun point of space creation needed specific procedure 
The planets were found before the sun creation and the planets revolve around a point in space (any point in space) the revolution creates two velocities on both sides of the revolution- the two velocities are equal in value opposite in direction- the total be Zero- means- the revolution motion creates a stationary point in the revolution center-
By that the sun point of space is created as a stationary point- and the sun point is the only stationary point in the solar system- for that all motions are done relative to the sun point of space- but let's ask
What does mean Pluto velocity is 4.7 km/s? it means – the sun point of space is a stationary point and its velocity is 1 km/s (Zero approximately)- and that means- the space around the sun has waves move by velocity 1 km/s while Pluto velocity is 4.7 km/s and that means the space around Pluto has waves move by 4.7 km/s  and by Pluto motion the waves around the sun moves by 4.7 km/s because of Pluto motion effect
Shortly- the sun is the stationary point in the solar system and all motions are done relative to the sun because it's the minimum velocity in the solar system.
II- The Comparison
The gravitational waves are reflected in the solar system three times
(From Neptune to Saturn) This Is The First Reflection
(From Uranus to Jupiter) This Is The Second Reflection
(From Venus to Mars) This Is The Third Reflection
Here we compare among the data of these planets- the comparison provides 7 groups of data in each group we compare the planets data because I want to prove that the planets use similar behaviors to produce their data – means- this all data is created based on geometrical rules which proves that there's one reason caused to create all this data and this reason is the gravitational waves reflection- In the comparison I start by Venus reflection (the 3rd one) then Uranus reflection (the 2nd one) and Neptune reflection (1st one) because Venus is very simple data and can be understood easily-
The Data Changes
 The gravitational waves reflection causes basic changes in the planets data let's refer to these changes in following
What's used as (A) before the reflection will be used as (1/A) after the reflection.
What's used as (a distance) before the reflection will be used as (a period of time) after the reflection
The velocities be squared –the rate (v1/v2) before reflection will be (v1/v2)^2 after the reflection.
The energy direction is changed by the reflection
The players of the rates of time are reflected also –
Notice – the gravitational waves reflection needs three planets –as we have discussed- the 1st reflection (from Neptune to Saturn) and between them Uranus – also the 2nd reflection (from Uranus to Jupiter) and between them Saturn–  and also the 3rd reflection (from Venus to Mars) and between them The Earth– that shows three planets are used in each reflection- the middle planet is effected also by the wave reflection as we will see in the data discussion – shortly – No reflection can be done by two neighbors planets - 
These changes are done with each reflection for the gravitational waves- the planets data proves this fact as we will see in the comparison of the data and the detailed analysis for the wave reflection.
Group Data No (I)
(1)
The gravitational waves are reflected from Venus to Mars – For that
Venus orbital circumference 680 mkm is Changed Into Mars orbital period 687 days
And
687 days x 2π        = 4331 days (Jupiter orbital period)
687 days x 4π        = 10747 days (Saturn orbital period) x 0.8
687 days x 6π x 2  =  25920 years (The Precession Cycle)
(2)
The gravitational waves are reflected from Uranus to Jupiter– For That 
Jupiter orbital circumference 4900mkm is Changed Into The  period4900 days
And
4900 days x 2π      = 30589 days (Uranus orbital period)
4900 days x 4π      = 59800 days (Neptune orbital period) (error 3%)
4900 days x 6π      =  90560 days (Pluto orbital period) (error 2%)
(3)
The gravitational waves are reflected from Neptune to Saturn–
BUT
The distance 1433 mkm is still a distance And
(1410 mkm = Pluto Neptune Distance)
1433 mkm               = Mars orbital circumference
1433 mkm   x 2π    = 9010 mkm (Saturn Orbital Circumference)
1433 mkm   x 4π    = 18048  mkm (Uranus Orbital Circumference)
1433 days   x 8π     = 37100 days (Pluto orbital Circumference) (error 2.5%)
Discussion
(1)
The data shows the following
The Gravitational Wave Reflection From Venus To Mars Defines Mars, Jupiter And Saturn Orbital Periods
(Saturn orbital period is effected by the rate 0.8 we should discuss later)
The Gravitational Wave Reflection From Uranus To Jupiter Defines Uranus, Neptune And Pluto Orbital Periods
The Gravitational Wave Reflection From Neptune To Saturn Defines Saturn, Uranus, Neptune And Pluto Orbital Circumference
This data proved my planet definition (the planets are geometrical points carried by the same one energy- or- the planets are geometrical points found on the same one light beam- and the planets move with this light beam motion- and the planets are created depending on each other and No planet is independent from the others in its creation and motion) – means- the planets are similar to whirlpools (vortex) found on the sea water page- we can imagine many whirlpools (vortex) are found on the same one sea and they are near to each other- this picture is very similar to the planets nature- that explains how the reflection of energy for one time can define the orbital periods for three planets (or 4 planets) together-
Here we imagine there are 4 whirlpools (vortex) on the sea page near to each other and then one strong wave of water passed through these 4 whirlpools (vortex), and this water wave motion causes effects on the 4 whirlpools-
This information is so important because one motion only (one wave reflection) can cause to define three or four planets data that proves strongly the planets Can NOT be independent neither in Creation Nor in motion- the planets are created and moving depends on each other because all of them are created from the same one energy and they move with this same energy motion-
NOTICE Let's imagine we have 4 whirlpools (vortex) on the sea page near to each other and one strong water wave passes through these 4 whirlpools (vortex)  - now – suppose we put some red color on this strong water wave- what would happen? The water color will be red and the red water will pass through these 4 whirlpools (vortex)  
We pay attention here because one reflection of energy can define the orbital periods of three planets – Means – all of them must be dependent on this reflected energy.
That tells the planets are NOT independent but they are dependent on the mother energy from which they are created and that caused they to be dependent on each other –
Now let's analyze each reflection individually
(1) The Third Reflection (The Wave Is Reflected From Venus To Mars)
224.7 days (Venus orbital period) is changed into 227.9 mkm (Mars orbital distance)
AND-
680 mkm (Venus Orbital Circumference) is changed into 687 days (Mars orbital period)- (max error 1.5%) –
As the rule tells (what's used as distance before the reflection be used as a period of time after the reflection and vice versa)
The orbital periods definition
687 days x 2π = 4331 days (Jupiter orbital period)
687 days x 4π = 10747 days (Saturn orbital period) x 0.8
687 days x 6π x 2  =  25920 years (The Precession Cycle)
We don't discuss the precession cycle here
(Saturn orbital period is effected by the rate 0.8 we should discuss later)
The data shows, the planets orbital periods are defined by the rates (2π, 4π, 6π)
It's not clear yet why the design uses these rates to define the planets orbital periods but this is the rule we will see it in the other two reflections of energy.
The important notice here tells that- the gravitational wave reflection for one time defines 3 planets orbital periods – this fact is proved strongly by the data and it disproves the wrong idea tells (Planet is created independently from the other planets) 
(2) The Second Reflection (The Wave Is Reflected From Uranus To Jupiter)
Here we have a clear problem – let's see the data
Jupiter orbital circumference 4900 mkm is Changed Into The  period 4900 days
And
4900 days x 2π      = 30589 days (Uranus orbital period)
4900 days x 4π      = 59800 days (Neptune orbital period)                    (error 3%)
4900 days x 6π      =  90560 days (Pluto orbital period)                       (error 2%)
We see clearly, the data distribution is typical to the previous data of the third reflection- let's compare them
Venus orbital circumference 680 mkm is Changed Into Mars orbital period 687 days
Jupiter orbital circumference 4900mkm is Changed Into The  period 4900 days  
687 days x 2π = 4331 days (Jupiter orbital period)
4900 days x 2π = 30589 days (Uranus orbital period)
687 days x 4π = 10747 days (Saturn orbital period) x 0.8
4900 days x 4π = 59800 days (Neptune orbital period) (error 3%)
4900 days x 6π = 90560 days (Pluto orbital period) (error 2%)
The comparison shows clearly the data is almost typical- by that- we have to suppose- the gravitational wave is reflected from Jupiter to Uranus- It is NOT Fact–because
The gravitational wave is reflected from Uranus to Jupiter (and then to Venus) – we see clearly the problem where the data distribution is reversed the wave reflection direction-
Notice - please note clearly that – we deal with one gravitational wave only- there are NOT three gravitational wave and each wave is reflected in one reflection- it's NOT Fact – the fact is that- it's one gravitational wave reflected three times in the solar system- the comparison next data proves this fact and gives no area for any doubt-
It's one gravitational wave sent from Pluto to Neptune and reflected to Saturn then this same wave is sent from Saturn to Uranus and Uranus reflected the same wave to Jupiter and Jupiter sent the same wave to Venus and Venus reflected the same wave to Mars- One Gravitational Wave moves through all these planets        
The Conclusion
The planets data is distributed in the reversed direction for the reflected energy- the energy is reflected from Uranus to Jupiter but the data is distributed from Jupiter to Uranus- there's a geometrical reason for this behavior we should discover later.
(3) The First Reflection (The Wave Is Reflected From Neptune To Saturn)
We still have another problem- let's remember this problem reason
The gravitational wave first reflection is done from Pluto to Neptune, supposing Neptune would send the energy to Uranus but Neptune didn't send the energy instead Neptune kept the energy inside its orbit and prevent it to move toward Uranus – also Uranus itself couldn't release the imprisoned energy from Neptune orbit – and that necessitated Saturn itself to create interaction with Neptune to release the imprisoned energy for that the energy is moved toward Saturn immediately by that this reflection of the wave is considered the first reflection because the energy is released from Neptune to Saturn directly – Shortly- the wave energy is sent from Pluto to Neptune and the energy is reflected from Neptune to Saturn and this is the first reflection of the energy (the gravitational wave first reflection)
Let's see the data - The distance 1433 mkm (Saturn orbital distance) is still a distance And (1410 mkm = Pluto Neptune Distance)
1433 mkm               = Mars orbital circumference
1433 mkm   x 2π    = 9010 mkm (Saturn Orbital Circumference)
1433 mkm   x 4π    = 18048  mkm (Uranus Orbital Circumference)
1433 days   x 8π     = 37100 days (Pluto orbital Circumference) (error 2.5%)
The data follows the rule (2π, 4π, 8π) perfectly as the other two reflections but the data shows 2 problems which are
1st problem
The data distribution is in the reversed direction of the energy motion direction- because the reflection is done from Neptune to Saturn but the data shows the orbital circumferences of (Saturn, Neptune, Uranus and Pluto) are defined by this reflection which supposes the energy is reflected from Saturn to Neptune and that's NOT Fact 
This behavior is typical the behavior of the second reflection from Uranus to Jupiter-
Means- this behavior is repeated in the two reflections of energy which tells that the behavior depends on a geometrical reason.
2nd problem
The distance is not changed into a period of time as the other reflections but stayed as a distance! How and why?? let's see deeply this data
If the energy is reflected from Saturn to Neptune, Saturn orbital circumference 9010 mkm should be changed into a period of time to be 9010 days and then
9010 days    x 2π    = 2 x 28244 days (28244 mkm = Neptune orbital circumference)
9010 days    x 4π    = 113223 days
9010 days    x 6π    = 169840 days
We see the data gives NO real values- means- this is not the direction of the data creation- Instead – the distance 1433 mkm or the circumference 9010 mkm is still distance and then
1433 mkm   x 2π    = 9010 mkm (Saturn Orbital Circumference)
1433 mkm   x 4π    = 18048  mkm (Uranus Orbital Circumference)
1433 days   x 8π     = 37100 days (Pluto orbital Circumference) (error 2.5%)
And
1433 mkm               = Mars orbital circumference
We understand that, the data provides a distance (1433 mkm) and not a period of time then we have to ask again why this distance is not changed into a period of time?
We understand that the outer planets have 2 reflections (first reflection from Neptune to Saturn) and (the second reflection from Uranus to Jupiter)- also we understand that the solar system needs one reflection only in the outer planets and one reflection only in the inner planets and also we know the outer planets have two reflections because of Neptune negative effect on the solar system- means if Neptune is removed from the solar system the outer planets would have one reflection only – for that- the designer caused the two reflections in the outer planets to be complementary one another – the reflection from Uranus to Jupiter defines the planets orbital periods and the reflection from Neptune to Saturn defines these same planets orbital circumferences
 The designer caused to make the two reflections complementary one another and by that the two reflections can be unified into one reflection and based on that the machine will work by one unified reflection in the outer planets and one single reflection in the inner planets- but how the energy motion produces the distances in place of the periods of time? this question is hard to answer because we don't see deeply how the reflection of energy can define each planet orbital period (or orbital circumference) by using the rates (2π, 4π, 6π) we just discovered the rule but more geometrical analysis is required to see how this rule works
NOTICE
In the third reflection (from Venus to Mars) – let's remember the data
Venus orbital circumference 680 mkm is Changed Into Mars orbital period 687 days
687 days x 2π        = 4331 days (Jupiter orbital period)
687 days x 4π        = 10747 days (Saturn orbital period) x 0.8
687 days x 6π x 2  =  25920 years (The Precession Cycle)
We have asked- why Saturn orbital period is effected by the rate (0.8)?
Let's try to answer – let's see the data 10747 /9800 = 9800/9010 where
10747 days  = Saturn orbital period and 9010 mkm   = Saturn orbital circumference
9800 mkm   = 2 x 4900 mkm (Jupiter Orbital Circumference)  
We know 4900 mkm and 4900 days is the player in the second reflection from Uranus to Jupiter- means- Saturn has effect also in the second reflection for that the second reflection has effect on Saturn data and caused its orbital period to be produced under the effect of the rate (0.8) which is the reflection rate as we will see in the next data 
Group Data No (II)
(1)
3.024 mkm (Venus motion distance per solar day) x 0.8   = 2.4 mkm
2.57 mkm (Venus motion distance per solar day)              = 1.0725 x 2.4 mkm
2.57 mkm x 0.8 = 2.082 mkm (Mars motion distance per solar day)
(2)
1.1318 mkm (Jupiter motion distance per solar day) x 0.8 = 2 x 1.0725 x 0.421 mkm
(3)
0.838 mkm (Saturn motion distance per solar day) x 0.8 = 2 x 1.0725 x 0.3129 mkm
Discussion
We discuss the data no. (2) and (3) at first
DATA NO. (2)
1.1318 mkm (Jupiter motion distance per solar day) x 0.8 = 2 x 1.0725 x 0.421 mkm
(0.421 mkm = Uranus motion distance in its rotation period)
DATA NO. (3)
0.838 mkm (Saturn motion distance per solar day) x 0.8 = 2 x 1.0725 x 0.3129 mkm
(0.3129 mkm = Neptune motion distance in its rotation period)
MORE DATA
0.5875 mkm (Uranus motion distance per solar day) x 0.8 = 0.46688 mkm
(0.466884 mkm = Jupiter motion distance in its rotation period) And
0.46688 mkm (Neptune motion distance per solar day) x 0.8 = 0.3736 mkm
(0.3736 mkm = Saturn motion distance in its rotation period) And
0.46688 mkm (Pluto motion distance per solar day) x 0.8 = 0.3248 mkm
(i)
The rate (0.8) is created by the waves reflection and the planets velocities are defined based on each other by this rate as discussed in the planet velocity definition-  here the data shows the rate (0.8) defines each planet motion distance based on the other planet motion distance (in the same one reflection) –
let's explain that in more details
(1st reflection From Neptune to Saturn) for that
Saturn motion distance per solar day (0.838 million km) by the rate (0.8) defines Neptune motion distance in its rotation period 0.3129 million km
Also
Neptune motion distance per solar day (0.46688 million km) by the rate (0.8) defines Saturn motion distance in its rotation period 0.3736 million km
AND
(2nd reflection From Uranus to Jupiter) for that
Jupiter motion distance per solar day (1.1318 million km) by the rate (0.8) defines Uranus motion distance in its rotation period 0.421 million km
Also
Uranus motion distance per solar day (0.5875 million km) by the rate (0.8) defines Jupiter motion distance in its rotation period 0.46688 million km
AND
In the 3rd reflection we will see Mars motion distance per solar day is defined by Venus motion distance per solar day- follows the same rule  
Notice
We note the data No. (2) and (3) show the data is distributed in the reversed direction for the energy motion because the energy is reflected from Neptune to Saturn and from Uranus to Jupiter- But data is distributed in the reversed direction-
In the third reflection we will see the data moves in the same direction with the energy distribution
Also  
In Venus data we will see that it uses the square value (0.8)^2 and we will explain why the rate is used in square value
(ii)
Why is the rate (1.0725) found in the data? because the gravitational wave  moves by speed of light (300000 km/s) in Saturn orbit and in all planets orbits till Venus orbit-
Shortly
the wave velocity was 205.8 km/s through Pluto, Neptune and Uranus orbits BUT
The wave velocity is accelerated in Saturn orbit and its velocity be = speed of light =300000 km/s, for that reason the rate (1.0725) is created because this is (Lorentz length contraction effect rate) and it can be produced only by motion with speed=(99% speed of light =297000 km/s)- shortly- the wave velocity be equal=speed of light = 300000 km/s in Saturn orbit, for that the rate (1.0725) is produced in the orbits of Saturn and Jupiter as the data shows (and also in Venus data we will see it)
(iii)
The previous data shows the planets distances are rated by the rate (0.8) for the planets players in the same wave reflection- but- this picture is not complete yet – because the planets which aren't players in the same reflection shows equal distances also but this distances equality doesn't depend on the rate (0.8) let's give examples
Jupiter motion distance in its rotation period = Neptune motion distance per solar day =0.466884 million km
And
Saturn motion distance in its rotation period 0.3736 mkm x π = Uranus motion distance per solar day 0.5875 mkm x 2
And
The Earth motion distance per solar day = Pluto motion distance in its rotation period = 2.574 million km
This distances equality must be produced also by the waves reflection but the rule is not clear yet- I want to say the effect of the rate (0.8) on the planets distances is part of greater rule explains how this distances equality is produced and the useful result of it –
Please note–I analyze this data in details in 2nd part of this 1st hypothesis explanation-
Now
Let's discuss the data No.(1)
DATA NO. (1)
3.024 mkm (Venus motion distance per solar day) x 0.8 = 2.4 mkm
2.57 mkm (The Earth motion distance per solar day)                  = 1.0725 x 2.4 mkm
2.57 mkm x 0.8 = 2.082 mkm (Mars motion distance per solar day)
2.57 mkm = The Earth motion distance per solar day= Pluto motion distance in its rotation period
Means
3.024 million km x (0.8)^2 x 1.0725 = 2.082 million km where
3.024 mkm  =Venus motion distance per solar day
2.082 mkm  =Mars motion distance per solar day
Notice
2.57 mkm = The Earth motion distance per solar day
2.57 mkm = 1.0725 x 2.4 mkm The moon motion distance per solar day
2.59 mkm = Pluto motion distance in its rotation period
The data tells Mars motion distance per solar day depends on Venus motion distance per solar day – here all distances are defined by the solar day- 
In the third reflection- the wave is reflected from Venus to Mars- here also Venus motion distance per solar day (3.024 mkm) defines Mars motion distance per solar day (2.082 mkm)- but the definition depends on the squared value (0.8)^2 
That shows Venus reflection follows the same rule used by the other reflections – where the sender planet motion distance per solar day defines the receiver planet motion distance
Perfectly the rule is followed BUT Why does Venus use the square value (0.8)^2??
Because of the reflections order – let's explain that
The two reflections in the outer planets are complementary each other and by that they are unified and can be considered as One Unified Reflection in the outer planets
Means- there is one unified reflection in the outer planets and one single reflection in the inner planets and these are two reflections- means – Venus reflection should be considered the second reflection that causes to square the value (0.8)- that explains why Venus uses the squared Value (0.8)^2
Notice
This is a proof for my theory that (one gravitational wave is reflected three times)- means- this wave is reflected before and effected by the rate (0.8) and this same wave is reflected again for that the rate (0.8) be in its squared value  (0.8)^2
The Conclusion
The gravitational waves reflection causes the sender planet motion distance to define the receiver planet motion distance as seen in the data- the definition depends on the rate (0.8) – here we see one rule proves the receiver planet motion depends on the sender planet motion- 
Group Data No (III)
(1)              
5.56 = (568/102) = (59800/10747)
(2)              
21.8 = (1898 /86.8) = 30589 /1407.6
(3)              
(4.87/0.642) ^2 = (7.6)^2 and (7.6)^2 x 224.7 days = 2π^2 x 687 days
And
π^3 = 31 = (5.56)^2 = 4x 4.75 (but between 7.75 and 7.6 the error 2%)
Discussion
Data No. (1)
5.56 = (568/102) = (59800/10747)
568 x 10^24 kg      = Saturn Mass
102 x 10^24 kg      = Neptune Mass
59800 days            = Neptune orbital period
10747 days            = Saturn orbital period
In the first reflection the gravitational wave is reflected from Neptune to Saturn
This behavior shows second rule– for the planets in the same reflection- we see the masses rate defines the orbital periods rate and this behavior is used by the other two reflections- means- the gravitational wave reflection between two planets cause these two planets masses rate to define their orbital periods rate – let's see the rest data
Data No. (2)
21.8 = (1898 /86.8) = 30589 /1407.6                   (notice1407.6π =4331 error 2%)
1898 x 10^24 kg    = Jupiter Mass
86.8 x 10^24 kg     = Uranus Mass
30589 days            = Uranus orbital period
4331 days              = Jupiter orbital period
In second reflection the gravitational wave is reflected from Uranus to Jupiter
It's the same rule and behavior, the planets masses rates defines their orbital periods
Just Jupiter orbital period 4331 is divided by (π) – no any other change in the rule proves that the rule is a fact and used with the planets of the same reflection
Data No. (3)
(4.87/0.642) ^2 = (7.6)^2 and (7.6)^2 x 224.7 days = 2π^2 x 687 days
4.87 x 10^24 kg     = Venus Mass                          and 0.642 x 10^24 kg= Mars Mass
224.7 days             = Venus orbital period              and 687 days= Mars orbital period
In the third reflection the gravitational wave is reflected from Venus to Mars
Here also we see the planets use the same rule and the same behavior – the masses rate defines the orbital periods rate-But the rate is squared! Why?   
Venus Mass = 7.6 Mars Mass but the data uses the squared rate (7.6)^2 –
We should pay attention for this rate because the other planets used their masses rate but NOT squared value – Why does Venus use the squared value (7.6)^2?
We have solved this question in the distances discussion when Venus used (0.8)^2 and the other planets use (0.8) only- here also is similar to that- let's remember the reason
We agreed that the two wave reflections in the outer planets are complementary one another and by that they are unified together into one unified reflection and by that the outer planets has one unified reflection and the inner planets has one single reflection and these are considered as two reflections and for that Venus reflection is considered the second one in the solar system (and the final one) for that Venus uses the squared Value – where we know the wave reflection causes to square the value
Notice - 5.56 = (568/102) = (59800/10747) = (10/1.8) =9010/1622 where 1.8 deg = Neptune orbital inclination and 10 =4 x 2.5 deg (Saturn orbital inclination) and -9010 mkm= Saturn orbital circumference and 1622 mkm = Neptune Uranus Distance
Notice π^3 = 31 = (5.56)^2 = 4x 4.75 (but between 7.75 and 7.6 the error 2%) – this data is discussed in the next point
The Conclusion The Wave Reflection Causes The Sender And Receiver Planets Masses Rate To Define Their Orbital Periods Rate.
Group Data No (IV)
(1)
12104 km (Venus diameter) /6792 km (Mars diameter) = 3.4 deg /1.9 deg = π^0.5
(2)
142984 km (Jupiter diameter)/51118 km (Uranus diameter) = 2.79 =5.56/2
(3)
378675 km (Saturn Circumference)/49528 km (Neptune diameter) = 7.6
Discussion
Notice
π^3 = 31 = (5.56)^2 = 4x 4.75 (but between 7.75 and 7.6 the error 2%)
This data shows the rates (5.56) and (7.6) are found based on the value (π^3=31) I try to prove that it's one energy (one value π^3=31) and the different rates as (5.56 and 7.6) are found depending on (this one value π^3=31) by geometrical reasons – that proves it's one energy (one wave) is reflected three times in the solar system – the value (π^3 = 31 =) is very important because all rates depend on it
The group data shows the planets diameters rates depend on the value (π^3 =31)- let's examine it in following
Data No. (1)
12104 km (Venus diameter) /6792 km (Mars diameter) = 3.4 deg /1.9 deg = π^0.5
3.4 degrees = Venus Orbital Inclination
1.9 degrees = Mars Orbital Inclination
The data shows the two planets diameters are rated with rate equal their orbital inclination and this rate equal π^0.5
Notice
177.4 degrees (Venus axial tilt) = 1.9 deg (Mars orbital inclination) x 93.4
90+ 3.4 = 93.4 deg
Data No. (2)
142984 km (Jupiter diameter)/51118 km (Uranus diameter) = 2.79 = 5.56
We remember 31 = (5.56)^2
Data No. (3)
378675 km (Saturn Circumference)/49528 km (Neptune diameter) = 7.6
Also we remember 31/4 = 7.75 (and the difference between 7.75 and 7.6 is 2%)
The data shows the diameters rates depend on the value (π^3 = 31 =) as the masses do
Means- the planets masses and diameters are created rated to one another based on this same value (π^3 = 31 =)
I try to prove that – one energy is found behind all this data- the value (π^3 = 31 =) refers to one energy and this energy is effected by different geometrical reasons and that causes this energy (π^3 = 31 =) to show different rates as (5.56) and (7.6)
Shortly – we deal with one energy reflected three times in the solar system and the planets data are defined by the effect of this energy on them
Please note- we can imagine one river of water moves through different cities and each city deals with the river based on its own data- one city has great soil and this uses the river water to plant vegetables and fruits- another city its ground has many holes and caves the river water will cause all these holes to be filled of water and that will create many moors in this city and that will not be useful for it –
We have here the same picture-
One energy moves through the solar system and reflected three times in it and this reflection causes changes for the planets data for that the different rates (5.56 and 7.6) are created from this one energy (π^3 = 31 =) by geometrical reasons have effects on it. (CONT)  
Gerges Francis Tawdrous +201022532292
Physics Department-  Physics & Mathematics  Faculty 
Peoples' Friendship university of Russia – Moscow   (2010-2013)
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timewaster4531 · 2 months ago
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Me today:
Walks into pre-calc
Teacher: ok class, now turn your computers away from each other for the test
Me: wait there's a test today?????
Me: frantically trying to copy the notes from the girl next to me
Gets_nowhere.jpeg
Test starts: i have no notes and did not study
Result: 100%
This has happened 3-4 times to me in this class (i cant remember if we've had 3 or 4 tests)
Also me: 60% on history tests because I cant remember anything ever
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etheral-moon · 3 months ago
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Guys maths are gonna be the end of me no joke
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astral-from-afar · 1 year ago
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just blacklist 'astral at work' if you wanna not see me suffer
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matias-2003 · 2 months ago
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The divisibility rules of every number from 401 to 500 with alternate methods for the composite numbers that end in 1, 3, 7 or 9
401: The difference between 40 times the last digit and the rest of the number is a multiple of 401
402: The number is a multiple of 2 and 201 at the same time
403: The sum of 121 times the last digit and the rest of the number is a multiple of 403
404: The number is a multiple of 4 and 101 at the same time
405: The number is a multiple of 5 and 81 at the same time
406: The number is a multiple of 2 and 203 at the same time
407: The difference between 122 times the last digit and the rest of the number is a multiple of 407
408: The number is a multiple of 8 and 51 at the same time
409: The sum of 41 times the last digit and the rest of the number is a multiple of 409
410: The number is a multiple of 10 and 41 at the same time
411: The difference between 41 times the last digit and the rest of the number is a multiple of 411
412: The number is a multiple of 4 and 103 at the same time
413: The sum of 124 times the last digit and the rest of the number is a multiple of 413
414: The number is a multiple of 2 and 207 at the same time
415: The number is a multiple of 5 and 83 at the same time
416: The number is a multiple of 13 and 32 at the same time
417: The difference between 125 times the last digit and the rest of the number is a multiple of 417
418: The number is a multiple of 2 and 209 at the same time
419: The sum of 42 times the last digit and the rest of the number is a multiple of 419
420: The number is a multiple of 20 and 21 at the same time
421: The difference between 42 times the last digit and the rest of the number is a multiple of 421
422: The number is a multiple of 2 and 211 at the same time
423: The sum of 127 times the last digit and the rest of the number is a multiple of 423
424: The number is a multiple of 8 and 53 at the same time
425: The number is a multiple of 17 and 25 at the same time
426: The number is a multiple of 2 and 213 at the same time
427: The difference between 128 times the last digit and the rest of the number is a multiple of 427
428: The number is a multiple of 4 and 107 at the same time
429: The sum of 43 times the last digit and the rest of the number is a multiple of 429
430: The number is a multiple of 10 and 43 at the same time
431: The difference between 43 times the last digit and the rest of the number is a multiple of 431
432: The number is a multiple of 16 and 27 at the same time
433: The sum of 130 times the last digit and the rest of the number is a multiple of 433
434: The number is a multiple of 2 and 217 at the same time
435: The number is a multiple of 5 and 87 at the same time
436: The number is a multiple of 4 and 109 at the same time
437: The difference between 131 times the last digit and the rest of the number is a multiple of 437
438: The number is a multiple of 2 and 219 at the same time
439: The sum of 44 times the last digit and the rest of the number is a multiple of 439
440: The number is a multiple of 11 and 40 at the same time
441: The difference between 44 times the last digit and the rest of the number is a multiple of 441
442: The number is a multiple of 2 and 221 at the same time
443: The sum of 133 times the last digit and the rest of the number is a multiple of 443
444: The number is a multiple of 4 and 111 at the same time
445: The number is a multiple of 5 and 89 at the same time
446: The number is a multiple of 2 and 223 at the same time
447: The difference between 134 times the last digit and the rest of the number is a multiple of 447
448: The number is a multiple of 7 and 64 at the same time
449: The sum of 45 times the last digit and the rest of the number is a multiple of 449
450: The number is a multiple of 9 and 50 at the same time
451: The difference between 45 times the last digit and the rest of the number is a multiple of 451
452: The number is a multiple of 4 and 113 at the same time
453: The sum of 136 times the last digit and the rest of the number is a multiple of 453
454: The number is a multiple of 2 and 227 at the same time
455: The number is a multiple of 5 and 91 at the same time
456: The number is a multiple of 8 and 57 at the same time
457: The difference between 137 times the last digit and the rest of the number is a multiple of 457
458: The number is a multiple of 2 and 229 at the same time
459: The sum of 46 times the last digit and the rest of the number is a multiple of 459
460: The number is a multiple of 20 and 23 at the same time
461: The difference between 46 times the last digit and the rest of the number is a multiple of 461
462: The number is a multiple of 2 and 231 at the same time
463: The sum of 139 times the last digit and the rest of the number is a multiple of 463
464: The number is a multiple of 16 and 29 at the same time
465: The number is a multiple of 5 and 93 at the same time
466: The number is a multiple of 2 and 233 at the same time
467: The difference between 140 times the last digit and the rest of the number is a multiple of 467
468: The number is a multiple of 4 and 117 at the same time
469: The sum of 47 times the last digit and the rest of the number is a multiple of 469
470: The number is a multiple of 10 and 47 at the same time
471: The difference between 47 times the last digit and the rest of the number is a multiple of 471
472: The number is a multiple of 8 and 59 at the same time
473: The sum of 142 times the last digit and the rest of the number is a multiple of 473
474: The number is a multiple of 2 and 237 at the same time
475: The number is a multiple of 19 and 25 at the same time
476: The number is a multiple of 4 and 119 at the same time
477: The difference between 143 times the last digit and the rest of the number is a multiple of 477
478: The number is a multiple of 2 and 239 at the same time
479: The sum of 48 times the last digit and the rest of the number is a multiple of 479
480: The number is a multiple of 3 and 160 at the same time
481: The difference between 48 times the last digit ans the rest of the number is a multiple of 481
482: The number is a multiple of 2 and 241 at the same time
483: The sum of 145 times the last digit and the rest of the number is a multiple of 483
484: The number is a multiple of 4 and 121 at the same time
485: The number is a multiple of 5 and 97 at the same time
486: The number is a multiple of 2 and 243 at the same time
487: The difference between 146 times the last digit and the rest of the number is a multiple of 487
488: The number is a multiple of 8 and 61 at the same time
489: The sum of 49 times the last digit and the rest of the number is a multiple of 489
490: The number is a multiple of 10 and 49 at the same time
491: The difference between 49 times the last digit and the rest of the number is a multiple of 491
492: The number is a multiple of 4 and 123 at the same time
493: The sum of 148 times the last digit and the rest of the number is a multiple of 493
494: The number is a multiple of 2 and 247 at the same time
495: The number is a multiple of 5 and 99 at the same time
496: The number is a multiple of 16 and 31 at the same time
497: The difference between 149 times the last digit and the rest of the number is a multiple of 497
498: The number is a multiple of 2 and 249 at the same time
499: The sum of 50 times the last digit and the rest of the number is a multiple of 499
500: The number ends in 000 or 500
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uncontrolledfission · 1 year ago
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Facts about Pi you probably didn't know
Post #19 on [Maths,] Physics and Astronomy, 16/07/23
I lied, my next post is not about nucleosynthesis in merging neutron stars. I watched a Veritasium video about how Pi was revolutionised and it totally had me encapsulated, so after some extra reading, here I am with some facts about Pi you weren't taught in school! I wish that we were taught about some of the fascinating history behind the maths taught in school. It's interesting as-is, but you'd think students would be a lot more engaged, right?
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Pictured: Ludolph van Ceulen, the German-Dutch mathematician responsible for calculating Pi to 35 digits of accuracy by bisecting polygons. In some places in Germany, Pi is sometimes still referred to as the Ludolphine number.
Archimedes of Syracuse is the man [somewhat] known for taking the most iconic bath in history. One day, he slipped into the bathtub and realised that the volume of water displaced was equal to the volume of his own body; realising this, he determined he could work out if a piece of jewellery was made of pure gold based off of its density. He realised the King of Syracuse's crown wasn't made of pure gold, and ran into the streets naked shouting, 'Eureka!' This has nothing to do with bisecting polygons, but it's a fun anecdote I wanted to share.
What he's better known for is being the first documented person to cook up a way to calculate Pi. To do this, he drew a hexagon, then a circle inside, and another hexagon inside that. The following diagram shows this:
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Here's the best explanation I can offer of this diagram. You see the circle? Assume its diameter is 1. Since the inner hexagon is equilateral, you can determine that its perimeter is 3 (each side is length 0.5). Using a method that's annoying to explain and essentially akin to early trigonometry, the outer hexagon's perimeter was determined to be 3√2. This already gives us an error interval for the value of Pi:
~3.46 > Pi > 3
Fascinating, right? Safe to say I'd never have thought of that. What's cooler is that, as shown in the diagram, the higher the number of sides in those polygons, the higher the degree of accuracy to which Pi can be worked out.
There comes van Ceulen, aforementioned. He spent 25 years of his life bisecting a polygon with approximately 32,212,254,720 sides, getting Pi to a grand total of... 20 decimals. This was later brought up to 30 decimals. These digits were engraved on his tombstone, rest his soul.
Following this, a great number of formulae to calculate Pi emerged. More commonly known is the infinite series.
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This formula also works out the decimals of Pi, and it was devised by Gottfried Leibniz and John Gregory. Pi, being the pinnacle of anarchy in maths, now had a strange sense of order to it. This formula essentially states that (Pi / 4) is equal to 1 minus a third, plus a fifth, and so on so forth. A relatively unproblematic formula could work it out.
It's worth mentioning that the infinite series was derived from calculus, also invented by Leibniz. However, Newton had also independently come up with calculus. A great deal of time was spent arguing over it; but old papers suggest it was an Indian mathematician named Madhava who had come up with it before them.
This formula isn't all too efficient. It took nearly 300 terms of the series to get Pi accurate to 2 decimal places.
However, the popularisation of calculus meant that other formulas had been created to work Pi's decimal places out. Then, it merely became a race of who could get the highest number. Any number of decimal places above 4 was unnecessary; engineers could do their job perfectly with Pi being 3.1415. It seemed as though the young, adventurous mathematicians of the age were concerned less about practicality, and more with the extent of their achievements. For that, I have a lot of respect.
Sources:
Veritasium, the discovery that transformed Pi
Alex's Adventures in Numberland, by Alex Bellos. (Book so I have no link.) Both latter images taken from the book.
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