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The answer is one right angle.

this is fantastic! watched many vids and this is the first time I have fully understood the types. very well executed, great teaching, thank you!

These cursed math videos caused me the damage equivalent to 7 norovirus epidemics

what does «bad joy» mean?

I don't know what's more cursed: the (often wrong) maths, or the music.

Is a Trigonometric Proof Possible for the Theorem of Pythagoras? Michael de Villiers RUMEUS, University of Stellenbosch CONCLUDING COMMENTS To get back to the original question of whether a trigonometric proof for the theorem of Pythagoras is possible, the answer is unfortunately twofold: yes and no. 1) Yes, if we restrict the domain to positive acute angles, any valid similarity proof can be translated into a corresponding trigonometric one, or alternatively, we could use an approach like that of Zimba (2009) or Luzia (2015). 2) No, if we strictly adhere to the unit circle definitions of the trigonometric ratios as analytic functions, since that would lead to a circularity.

hello, for B1a) why isit (D-2) instead of just subbing in -2?

Hello Joel, how did you get π/4 - 1/2 for B4b?

you should've added 2⁰ + 2¹ + 2² + 2³ + ... = -1

Bro doesn't know the definition of an equation. None of those are equations, they are identities. An equation is a mathematical statement with some variables, which holds for a finite number of values of those variables.

Very elegant!🎉 My teacher didn't show interest when I told him I had a similar proof in 2022.😢 It's been almost 1 year now. I'm out of high school now.

alternatively, ln(-1) = ipi

1+1-1+-1..... Diverges.

The nested radicals also work with any other number. Because in the end, you multiply a root of a number with the root of the same number.

ln(−x) = ln(−1 · x) = ln(−1) + ln(x) = ln(x) + π · i

I prefer: \int_{0}^{\infty}\sin x \:dx=(-\cos x)\Big|_0^\infty=-\cos\infty -\cos 0=-\cos\infty-1=\textup{Interval(\{-2;0\})}

The césaro sum is actually wrong

Wow it makes so much sense...Thank you so much ❤.. It was so good... I wanna use to improve relationship and also help people around me improve their relationships. Great work.

For the record, the cowboy hat was from Animation vs Physics, which is the previous installment of the Animation vs Science series. I highly recommend watching that one, as well.

The last object linked to the black hole of the last video

I saw this video That you watching last night

i know every bit of geometry of this video.

nice one .... but please make use of pause in future reactions ... so you can go in depth to concepts you like or wanna talk about

What you saw of himself with the cowboy hat, it is a reference to his previous animation which is animation vs physics

Oh

I suddenly feel like Alan and Terkoiz are inadvertently gonna bamboozle a lot of mathematicians when they show them a 4D object being contained by 3D structures. They already have a lot of laymen bamboozled it seems, along with themselves (°▽°;)

Before this video, I was only familliar with the yellow and pink parts of the graph. I'm surprised how much I learned! Thank you!

According to the creator, the golden shapes are equivalent to the golden ratio.

Wait.... you're a fan of Alan Becker, KindiakMath?! If you are, then so am I.

That was really well explained for how fast it was. And yeah, to explain, they were containing the 4D object inside a 3D shape, made out of 2D polygons. Pretty fun.

yooo a good theory

You called the Octohedron Icosahedron Called the Icosahedron Dodecahedron Forgets Dodecahedron

literally watching this in my bathroom

a guy that's also an asian and an indian?

W math teacher

This fella not only helped me with math but paid for all my tuition fees for poly 🔥🔥🔥

This is the "waffle cone" part of their proof: (I can't post a link.) Search: "math.stackexchange Is this series representation of the hypotenuse symmetric with respect to the sides of a right triangle?"

It's called a geometric series and scaling. It's infinitely repetitive. It says a^2 + b^2 = C^2 because a^2 + b^2 = c^2 over and over and over again for infinity. It's was already done in a previous proof: www.cut-the-knot.org/pythagoras/Proof100.shtml

How is this not a copy of John Arioni's "Pythagorean Theorem via Geometric Progression" proof (proof 100) at the cut-the-knot?

Actually, there is a somewhat simpler proof of the Pythagorian theorem, along similar lines, pictured in an ancient Sumerian (or Babylonian?) cuneiform clay tablet of about 4000 years ago. What it depicts is the subdivision of a right triangle into an infinite sequence of similar sub-triangles related sequentially in size by a common scaling factor r <1. Summing the lengths of the segments into which this divides the hypotenuse, using the formula for an infinite geometric series, gives the Pythagoras theorem. This method of proof, if interpreted correctly, seems to have been known already 4000 years ago. An article discussing this archaeological discovery was published in a Swiss (?) anthropological/archaeological journal about 50 years ago, but I do not have a copy, or the exact reference. Would anyone be able to track it down? A detailed presentation of this proof can be found in the RUclips video: "Sumerian/Babylonian proof of Pythagoras' theorem based on summation of infinite geometric series" at :ruclips.net/video/7642iBEOjCk/видео.html

1/x*ln(x) and 1/ln(x) should be noted as well, since one gives you a nice integral of ln(ln(x)) while the other opens a whole different field of math :DD

Linear ❌ Line-uh ✅

Wow🤩🤩🤩

As a student overwhelmed by high school geometry, this video of yours really shows the beauty of using geometry! I can rest assured that high school geometry does lead to somewhere beautiful

omg my mind is blown so this is how the real and imaginary axis came about

Nice proof we can prove cosine law without any circular reasoning or without Pythagoras theorem

Hey there, I have been watching you for so long now. You have great content. I have a proposal for you and is there anyway I can contact you?

The style of your video is very reminiscent of that of 3b1b! Nice video!

interesting :D😍