#Mathematics Lessons

[mathsprogram]

Online Math Tutor

Use our online tutors to unlock math success. Math mastery is made convenient with specialized instruction, professional supervision, and interactive learning. Join us for individualized online math tutor instruction that will help you develop the knowledge and self-assurance you need to succeed in school.

[simplydnp]

who's hand is in this picture?

A Mathematically Rigorous Proof That I Spent Too Long Writing

welcome to university math: dnp hand edition

(no, don't leave, you'll be fine i promise)

to begin, we need a statement to prove. we have two options:

- the hand is dan's hand

- the hand is phil's hand

now, for most proofs in university math, you are told a true statement, and you must show why it is true using logic rules, definitions, and theorems. but, we do not know which of these statements are true, so we have to find out.

to prove that a statement is true, we must show that it is always true for the situation presented. to show a statement is false, we must present a single instance where the statement is false (also known as a counter example).

a quick not scary math example:

definition: a prime number is only divisible by 1 and itself.

statement: all prime numbers are odd

(this is false, because 2 is a prime number and it is even. you don't even need to check if there's any others, all you need is one single case where it isn't true to disprove it)

so now that we have a little background on proofs and how to prove and disprove them, we go back to our two statements.

the thing with this situation is, one of them must be true (unless you're gung-ho on someone else holding dan's face while phil takes a picture on his phone of dan in his glasses, in which case, i applaud your commitment, but in actuality this proof will cover that option too)

the full statement we have is: dan is touching his face or phil is touching dan's face

now, because this is Real Life and we have a picture where a hand is touching dan's face, we know already that one of these options is true (as mentioned above) but! using symbolic logic you could also come to this conclusion.

this type of statement is an 'or' statement, and if you're curious, you can look into 'truth-tables' and see why, but at least one of the options must be true.

back to the proof at hand (bah-duhm-tss)

okay. now, proofs also must be 'general' in order to mean anything, really. these are statements of truth of the universe, not just for individuals. so, we will prove this generally.

we have 2 people involved, so individual 1 (dan, the owner of the face and potential face toucher) will be labelled as 'D' , and individual 2 (phil, the possible face toucher who does not own the face) will be labelled as 'P'. thus, this can be true for any such D and any such P.

so with our 'or' statement, in order to prove it, we pick one of the options and say that it is not true, and we have to show then that the other is true.

step 1: let's assume this is not P's hand. (assumption)

step 2: thus, it must be D's hand. (what we take from our assumption)

step 3: now, if it is D's hand, we look at what a hand on one's own face is capable of appearing like. (a definition or true fact about step 2)

the position in the given photo shows the hand with a thumb on the cheek, and a finger on the forehead. so, we find an example of a person with their fingers in the same position (or close to) and see if this supports our claim.

consider:

now, with this image, you can clearly see how the subject's right hand has the thumb on the temple and index finger on the top of their head, however, it is a close enough position for our case.

from the view of the camera, the closest finger to the camera is the edge of the pinkie. in fact, it will always be the closest finger to the camera in this position, assuming the subject has all fingers and no additional appendages.

step 4: we now compare this to our photo (we verify if this holds to our claim or contradicts it)

in our photo, the closest appendage to the camera is the edge of the thumb.

step 5: thus, it cannot be the case that D is touching their own face. (what the evidence says)

step 6: as we assumed it was not P's hand and have shown it cannot be D's hand, and as this is an 'or' statement both of these claims cannot be false, we can therefore conclude it must be P's hand. (our conclusion: re-stating the statement and assumptions and conclusion)

step 7: we verify that P is true (optional step but in beginner proofs you generally show why your case works)

to do this, i will show a picture of a person touching another's face, and compare it to our image.

consider:

now, this image is not exactly the same, similar to above. however, P's left thumb is on the cheek, with their index on D's temple. the closest appendage to the camera (if it were in a similar perspective as our original) would be the edge of the thumb.

comparing it to our original:

our comparison holds.

thus, we can conclude that the true claim in this statement is that P must be touching D's face, which, in particular means that:

phil is touching dan's face in the image

thank you for partaking in phannie mathematics. we now know. i am not sorry.

bonus:

phil has a hitchhikers thumb and dan doesn't so why was this necessary at all 🤡

[rad-roche]

a big time saving thing i've started doing with comics is i filled a big 5000 x 5000 canvas entirely with that scratchy texturing i do and whenever i need a big block for a comic or panel and it doesn't have to be too detailed i just copy paste a wad in. who will know? well, everybody reading this. but what court in the land will convict me

[amourlashai]

The Tao of Wu by RZA is such an intellectually stimulating book! I literally cannot stop highlighting because there are so many gems in it.

[dramsstuff]

😢🤔

[quotelr]

Mathematically, the purpose of life is to produce a result. In human terms, it is called Happiness.

Joey Lawsin, Creation by Law

[competitive-test]

10 Important MCC operation for competitive test

Squaring Numbers Ending in 5 🔢

✅ Easily square numbers that end in 5

👉 Example: 35²

Multiply the first digit by itself +1 → 3 × (3+1) = 3 × 4 = 12

Add 25 at the end → 1225

So, 35² = 1225 🎯

JOIN US AT Competitive Test Prep 👈.

[fivepercentgodsandearths]

Peace.

If You're interested seriously looking for Gods and Earths in your area. We are all over social media and use old flyers.

Beware

*There are others posing as us, calling themselves Muslim Gods, Saying we should be Under the Nation of Islam.

* Also should no True and Living, teach for sex or money. Your cost is time, determination and striving to live out the teachings daily.

*Also Your Ideas will be challenged, so you need to develop a thick skin.

*You will be required to read, books, articles etc.

*Skin color doesn't make you more Righteous. Words and actions should match

[dnaayan]

How important the mathematics is for asvab test?

Math is super important for the Armed Services Vocational Aptitude Battery especially if you're aiming for a high score or a specific job (MOS/AFSC/Rating) in the military. Arithmetic Reasoning including Word problems involving basic math, percentages, ratios, time, distance. Mathematics Knowledge including algebra, geometry, order of operations, fractions.

GET FREE VIDEO TUTORIAL 👈.

   Find the domain and range of the function:    f(x)=√(x-3)

If you need strong knowledge in mathematics. Try to see video tutorial. I think you will get more clear idea.

[thrill-kill-kult]

Music taste is such an interesting form of individuality. Like I love learning about different peoples’ music tastes because everyone finds such cool and diverse shit to listen to and like it’s so unique. Even if you have a lot of overlap in artists and genres with someone they’re still just about guaranteed to know and love some crazy niche artist you’ve never heard of.

[cereshazelnut]

making lessons in school as humans!

(also they havent had a ref sheet. maybe i need help for this)

[strawhatboy]

I will start teaching on monday! so excited, wish me luck besties <333

[gouinisme]

gonna kill this teacher

[inspired-lesson-plans]

Math, 6.G.A.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Do Now:

Students pick one random country using the Random Country Picker from pickerwheel.com, then go to Wikipedia and search "geography of [country]", and record their assigned country's area in square kilometers.

Class Discussion:

Ensure all students successfully found their country's area. Discuss ideas of how cartographers may have figured out their country's area.

Modeled Learning:

Pick a country at random on the SmartBoard, then pull up en.wikipedia.org/wiki/Geography_of_[country] .

Show how to trace over the country using paper, ruler, and pencil.

When doing so, make it clear that the goal of today's activity is to draw an overly simplified polygon, like the France hexagon example in the first response to this post.

Show how to use the scale provided on the map (which should be on every country found this way) in order to measure the side lengths of the superimposed polygon

Use the side lengths to calculate the area of the polygon.

Calculate the difference between the area of the polygon and the official area of the country.

Draw a more refined polygon, like @vang0bus did, and show how to break this down into simpler polygons (such as triangles and trapezoids), in order to recalculate the area. How much closer is this method to the official area of the country?

Higher Order Learning:

Students perform the activity that you modeled. If they finish with time remaining, encourage them to keep on refining the polygon to get as close to the official area as possible.

why is france called the hexagon when its abundantly clear that it’s a pentagon

[dramsstuff]

Let’s see how your brain works 🙂