Five Classic Proofs without Words

Рет қаралды 8,390

9 ай бұрын

In this video, we show animations of five famous/classic/iconic proofs without words: the formula for the sum of the first n integers; the formula for the difference of two squares; the formula for the sum of the first n odd integers; the pythagorean theorem using negative space/sliding rectangles/Chou pei suan ching; and the infinite geometric series of positive powers of 1/2 (using a rectangle/square dissection of a unit area square).
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This is a longer version of this short:
• Four famous proofs wit...
For videos with related animations, see
Summing Integers: • A Dozen Proofs: Sum of...
Pythagorean Theorem: • Ten Epic Pythagorean P... (and old version: • Pythagorean Theorem II... )
Summing Odds: • Sum of odd integers: a...
Geometric Series: • Beautiful Geometry beh...
The first proof was known to the ancient greeks (cited by Martin Gardner), the second proof is a classic that appears in numerous places (and was likely known to Arabic mathematicians); the third is attributed to Nicomachus of Gerasa by Roger Nelsen; the fourth proof is adapted from the Chou pei suan ching (around 200 BCE according to Roger Nelsen); and the final one is attributed to Warren Page (from the September 1981 issue of Mathematics Magazine, page 201 - www.jstor.org/stable/2689632 ). The first three can all be found in Roger Nelsen's first compendium, "Proofs Without Words: Exercises in Visual Thinking:
(I may receive a small commission at no cost to you for this affiliate link): amzn.to/40cQL3k
bookstore.ams.org/view?Produc... .
#math #manim #pythagoreantheorem #pythagorean #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo #geometricseries #infiniteseries #finitesums #infinitesums #oddsumformula #sumsofintegers #sums #shorts
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Пікірлер: 33

@StudywithmeinPakistan 9 ай бұрын

I wish we had such animations in our time in 1999 when I was doing my engineering. Now adays education is becoming more easier than ever before. Great channel. Watching from Pakistan 🇵🇰.

@MathVisualProofs 9 ай бұрын

Thank you! Happy to have you watching. 😀

@AutoDisheep 9 ай бұрын

We think its easier now, but I think people are getting more of an appreciation of the math

@Math_Rap_and_GOP_Politics 9 ай бұрын

Yes, mathematical education may be more easily taught by those few who appreciate this new technological insight. However, here in the U.S., mathematical understanding has plummeted. This lack of understanding has led my citizens unaware of the great spectacle which this channel encompasses.

@StudywithmeinPakistan 9 ай бұрын

@@Math_Rap_and_GOP_Politics Indeed.

@ZanderzMcCluer 9 ай бұрын

Beautiful. This video and this channel are amazing!

@MathVisualProofs 9 ай бұрын

Thank you so much!

@firegreat3420 9 ай бұрын

This channel is underrated

@MathVisualProofs 9 ай бұрын

👍😀😎

@shubhambawane199 9 ай бұрын

Thank you for creating Visual videos of math

@MathVisualProofs 9 ай бұрын

Happy to help!

@zareebplayz2844 9 ай бұрын

So beautiful and fascinating

@MathVisualProofs 9 ай бұрын

Thanks!

@PhilosophicalNonsense-wy9gy 5 ай бұрын

Beautiful

@MathVisualProofs 5 ай бұрын

Thank you

@phiarchitect 9 ай бұрын

very inspiring!

@symsoup 9 ай бұрын

Amazing style!

@MathVisualProofs 9 ай бұрын

Thank you!!

@anyoung1818 9 ай бұрын

This best channel in the multiverse!? 😮

@MathVisualProofs 9 ай бұрын

👍

@jakobthomsen1595 9 ай бұрын

Nice! Also in case you are looking for ideas for future videos: it seems you haven't animated the greatest common divisor algorithm yet. I think the GCD applied to a couple of examples would make a nice visualization.

@MathVisualProofs 9 ай бұрын

Yes! Euclidean algorithm does make sense to try. Thanks!

@abdelrahmanjoumaa2174 9 ай бұрын

I realy admir what you do 🎉🎉🎉 You must be an artist , this is the first time in my life when enjoy seeing a mathematic demonstration (by the way could you make a video about the logique of the sommation 1+2+3+4+............=-1/12) I saw this resulat multiple times and i cant understand how the somme of postive numbers can be negatif .😢😢😢😢😢😢

@academyofuselessideas 9 ай бұрын

Pretty cool... I have been wondering about the difference between verifying proofs and understanding them... These proofs can be done by algebraic methods (symbol-pushing) which is (arguably) the preferred method of standard mathematics/ But I wonder whether the symbol-pushing helps to understanding more than the geometric approach of this video. It is like the following Atiyah's quote: Algebra is the offer made by the devil to the mathematician. The devil says: "I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine." -Michael Atiyah

@MathVisualProofs 9 ай бұрын

Good to try to work with multiple ways of understanding to get a full sense of a particular idea :)

@academyofuselessideas 9 ай бұрын

good point... to quote Micheal Atiyah again: "I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs, the more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalise in different directions -- they are not just repetitions of each other."

@MathVisualProofs 9 ай бұрын

@@academyofuselessideasand there are at least 300 proofs of quad reciprocity now!

@mathemitnullplan 9 ай бұрын

indirect pythagorean is the best.

@RicardoGonzalez-tg3lw 9 ай бұрын

When I see these videos I can only think of how smart the guys that came up with these stuff were! And we're (most of us) now all just a bunch of idi0ts trying to understand it in the 21st century.

@Luizabf 9 ай бұрын

Muito bom

@MathVisualProofs 9 ай бұрын

😀

@ManishKashi 2 ай бұрын

Can you please share source code. And watching from India 😊

@Atmatan_Kabbaher 8 ай бұрын

Can you help me graph / animate a set i designed? Also, maybe help point me to learning how to graph z transform fractal equations?? Im really struggling taking my work to its next level, entitely lacking a formal edication, and all..