#Mathematics Lessons

[mathsprogram]

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[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]

😢🤔

[motherfactorin-pi-face]

In which I describe the maths of how to attack and dethrone God (per Minamimoto)

So in my evergrowing post thread (which I know I'm already gonna have to add to that essay fml) I did make ref to...well, a thing that literally has made my jaw drop since when I played TWEWY the first time (and keeping in mind this was a game friends forcefully insisted I play because "there's a char Sho Minamimoto who's just like you fr", and after I'd nodded "yup" re the SI unit obsessions and the compsci refs to Heaps and Crunching (and later, as I found out, "crashing" in JP), and the aesthetic, and, and...)

Namely: Sho Minamimoto literally uses (or tries to use) a very famous maths formula called Euler's Identity to take out the Composer as an example of Forcefully Applied Mathematics. :D (This may have also been the moment when I was like "Yup, he just like me FR")

So. First off. Euler's Identity.

It's kind of difficult to explain why this particular equation is considered one of the true Chef's Kisses of Mathematics to non-mathematicians, but part of it is elegance, and part of it is that it includes five of the foundational variables that show up in mathematics all the time (and really even more functions if you break it apart): a) the natural logarithm e or Euler's number which is roughly 2.71828182845... and which is zetta important in a lot of fields including finance, biology, medicine, and calculus functions, and (as we'll get into) antennas and field strength measurements and pretty much a Shitload of functions related to growth b) the imaginary unit i or the square root of -1 (which turns out to be extremely useful in a lot of contexts, including electronics (seriously; AC electricity and functions relating to that are *heavily* dependent on the imaginary unit) and graphing and arguably how Cartesian graphs work especially once you get into calculus c) Pi (π), everyone's favourite circle ratio of 3.141592653589793238462643393279 (is pulled away from keyboard before I can draw a Taboo Noise Refinery Sigil in Paint) and which is Important in many, many contexts d) 1 (yes, 1 is considered a constant! Specifically "A quantity exists") , and

e) 0 (yes, 0 is considered a constant too, specifically "a quantity does not exist", and reducing Euler's Identity results in e^(i*pi)+1=0) To make it even more Minamimoto-esque, you can technically also express Euler's Identity as a reduction of "e^(i*x) = cos(pi) + (i * (sin(pi)) (aka Euler's Formula), and cos(pi) =-1 and sin(pi)=0.

And really it's kind of a beautiful way of how things all fit together in a lovely function that is almost a kiss from the Math Gods and if plotted traces a lovely circle.

So after that little tangent, here's how this all relates to W2D7 of TWEWY, and Minamimoto's forcefully applied mathematics. * * * So, first we end up at Pork City (Mark City if you're watching the anime; Tokyu Group liked the TWEWY tourism and by the time the anime and NEO came around decided to take advantage of the advertising), and...Joshua and Neku start having a very interesting conversation on why there's So Much Damn Noise at Pork City anyways:

Neku asks if this is the work of Pi-Face, Joshua notes "Probably" and then goes on to note that it might not all be JUST Minamimoto:

In other words: Pork City is effectively acting as an amplifier or at least an antenna for Noise. (I am not the only one to have noticed it and not even the only one on Tunglr, for that matter; Voice From The Corner also picked up on this as well though I'll freely admit I'm diving a bit more into the STEM portions of this.) TWEWY:tA is even more blatant about this imagery in ep 6, where Joshua explicitly notes that all the emotion in Shibuya collects at Mark City (remember, the animation uses the RL name) and then "crashes into Mark City and shoots up into the sky. That emotion flows back down and keeps building up here." (Shortly afterwards, Joshua also mentions the Imaginary Noise Plane as the inside of Mark City warps, similarly to a sine wave flow--or the flow of energy into, or out of, an antenna. (You do not know how loudly I screamed seeing this, as an aside) So, this is where we get into piece one, e (and where a healthy interest in radio and electronics hobbies helps!)

So antennas, interestingly, have how well they pick up a frequency measured in a logarithmic scale, and basic field strength measurements (and a lot of other "wavey" things, including earthquakes, including, well, literal background noise) get measured on logarithmic scales too. It's rather more common with antennas and earthquakes for this to be measured on log-10 scales (hence the Richter scale for quakes, or decibels for antennas and sound). There's a particular group of measurements (physical field and power measurements), however, that actually uses log-e, aka the natural logarithm, and especially for voltage or current and "root power quantities"--the neper. And, in Euler's Identity, e is taken to powers...and Pork City is basically acting as a huge antenna. Also in info engineering aspects, there's another aspect--the nat, which is considered a unit of information or info entropy...also based on e. (I told you Euler's number comes up a lot of places!)

Let's continue... So now we come to i, the imaginary unit, and that's called out blatantly by Joshua:

This, too, is based on math--from Final Fantasy II, specifically, and how the Flare spell worked. Flare is an area-effect spell and it hit based on (Enemy's HP/Flare level), i.e. enemies that had HP divisible by 2 could be hit by a Flare level 2 spell and could deliver damage based on that spell's level, etc. So a level i Flare, based on how complex numbers work, could hit just about anything (assuming, of course, that the Composer is not a Fractal Bastard and promptly yeets himself into a PokeYugiBeyBladeVerse). But...that's not the ONLY part where things imaginary come into play. So, one of the interesting bits of lore that came out in (of all things) the NEO:TWEWY Field Walk RPG (alas, JP only, but a delightful source of lore, and thankfully the fan community preserved almost all of it) is actual canon on how Tin Pins and Psychs work including the actual formula on how they work in a convo between Minamimoto and Fret:

Fret: Soooo, these psychs and pins and stuff… how does it all work? Minamimoto: The pin is charged by the Imagination of the user. Fret: Uh huuuh. Minamimoto: The pin itself is just a medium. Fret: Mm-hmm. Minamimoto: “Power” is calculated from the numerical limit of the pin, using your will as a coefficient. Fret: Yeah. Minamimoto: But that formula alone means nothing to me!

(Emphasis mine: props to Pavaal on the Dead Bird App for initial translation, and to multiple others for confirmation from the FWRPG script.) So basically how Psychs work is functionally as an athame, using formula Psych=Limit^Imaginatio. (Secret Report 1 in TWEWY also confirms Imagination is important in making a Psych work to begin with; the formula) Of note, Minamimoto also has a canonically high Imagination, as detailed in the Secret Reports. To even become a Reaper to begin with (as noted in SR7) those who survive the week who have enough Imagination become Reapers, and even among Reapers Minamimoto tends to stand out (he is canonically the youngest Reaper Officer ever, and apparently had quite the rapid rise to power). SR15 in TWEWY notes (even keeping in mind that in this instance Hanekoma is being a bit of an Unreliable Narrator in covering his own butt regarding the Taboo Thing):

The sigil Minamimoto drew was one of the undecodable types. Was that a mistake on the Fallen Angel's part? Or was it a transcription error by Minamimoto? Either way, with that design, he stands little chance of reviving himself. However, Minamimoto is driven, and his Imagination strong. Perhaps strong enough to make a Taboo sigil work, even in the Underground... If so, the specific result would be impossible to predict.

And in SR19 (again, covering up just a bit for his own helping hand):

I've detected an energy spike here. It would seem Minamimoto has returned. I judged his revival unlikely after spotting his Taboo refinery sigil on the first day, but it appears Minamimoto's Imagination is much stronger than I'd anticipated. The Fallen Angel must have completed the array for him. A troubling thought. Who can say what impact this will have on the Composer and Conductor's Game?

And even in the NEO Secret Reports it's noted his second trip through Coco's version of the Sigil actually ramped up his Imagination even more (in NEO SR 7):

Minamimoto, on the other hand has all but vanished from the proxy’s side. His Noise refinery sigil drastically heightens his Imagination, which may be why he can clearly recognize the proxy’s abilities. I have an idea of what he’s planning. It’s dangerous, but I have no way of stopping him.

And again, TWEWY:tA also makes it more blunt that Minamimoto was selected explicitly because of his Imagination and his connections to Shibuya as Hanekoma's Plan B. So there's imaginary units (in the sense of literal level i flare), and imaginary units (in a Reaper whose Imagination is already in the stratosphere). And in regards to pi? Well, Pi-Face, he has very much a rep of being....numbers- and math-obsessed even BEFORE he throws 156 digits of pi in the Composer's face:

But pi (as a number) is actually meaningful as HELL to Minamimoto, he engages in saying pi to himself drawing the Taboo Noise Refinery Sigil (goroawase in Japanese which relates to literally an obstetrician going to a foreign country and a woman giving birth at night as insects make a lot of noise which can almost be seen as a minor ritual to Make It Work, a little happy pi rhythmic thing in English in the game, actual spoopy sounding pimetry in the anime that sounds very sorcery-y). Looking (for far too long) at the Taboo Noise Refinery Sigil, pi is encoded in it in at least four or five places (multiple times as functionally a magic binding circle, at least once where he draws the symbol for pi in such a way that when it's turned upside down it literally spells "pi"). It's important. It's meaningful. It's His Number and transcedential and irrational and beautiful and unrestrained :D So now y'all are wondering, "OK, smartass, where's the -1 at?" As I noted, another way you can write Euler's Identity is specifically as "e^(i*pi)+1=0", so that can be expressed as a way to null the Composer (who is probably the 1 in question). Euler's Identity would be used to subtract 1 from the equation, in other words (as Minamimoto was intending to come back from Erasure by literally integrating himself via Taboo Noise Refinery Sigil). There's one other interesting bit of symbolism, one that's deep enough that I'm not even sure the writers of TWEWY intended, but if so...it's such a chef's kiss that I have deepest admiration.

So Euler's Identity can be expressed in terms of a formula, and as a reduction of sine and cosines involving pi and i, but it can also be mapped as motion--specifically as how a function evolves. (I tend to be a pretty visual thinker, and there's an extremely good discussion on Euler's Identity here that goes into the whole "mapping the function" aspect to show how Euler's Identity works in practice.)

So typically when you're doing a non-negative function or a zero function, generally there's an assumption of "right-hand" rotation or movement. Complex functions, you get into fun things like circles, and curves, and even some very beautiful fractals (like with the Mandelbrot set) with the right iterative formulas. Euler's Identity...is literally a left-hand-path function:

(And those of you who were writing about the Cyclic Nature of Minamimoto are probably all screaming right now) Anyways, wanted to share in full one of the things that was a jawdropper for me in TWEWY back when I found the game at a glorified skateshop that sold games in 2011. Thank you for coming to my TED talk, zeptograms :3

[quotelr]

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

Joey Lawsin, Creation by Law

[cereshazelnut]

making lessons in school as humans!

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

[nymphnana]

[strawhatboy]

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

[gouinisme]

gonna kill this teacher

[mathsprogram]

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[asegbolu]

Addition and Subtraction of Fractions Mathematics JSS 1 First Term Lesson Notes Week 8

Subject: Mathematics Class: JSS 1 Term: First Term Week: 8 Age: 12 years Topic: Addition and Subtraction of Fractions Duration: 40 minutes Behavioural Objectives By the end of the lesson, students should be able to: Add fractions with the same and different denominators. Subtract fractions with the same and different denominators. Keywords Addition, Subtraction, Fractions, Common Denominator,…

[forgottenbones]

Why the UK has a problem with maths | FT Film

[dramsstuff]

What’s your answer!?😌