Top four visual proofs?
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- Опубликовано: 5 окт 2024
- In this short, we show animations of four of the most famous proofs without words: the formula for the sum of the first n integers; the pythagorean theorem using negative space/sliding rectangles/Chou pei suan ching; the formula for the sum of the first n odd integers; and the infinite geometric series of positive powers of 1/2 (using a rectangle/square dissection of a unit area square). We include brief justifications for these visual proofs.
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For a slightly different version of this short without words, see:
• Four famous proofs wit...
For longer 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 adapted from the Chou pei suan ching (around 200 BCE according to Roger Nelsen), the third is attributed to Nicomachus of Gerasa by Roger Nelsen, and the final one is attributed to Warren Page (from the September 1981 issue of Mathematics Magazine, page 201 - www.jstor.org/... ). The first three can all be found in Roger Nelsen's first compendium, "Proofs Without Words: Exercises in Visual Thinking: bookstore.ams.... .
#math #manim #pythagoreantheorem #pythagorean #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo #geometricseries #infiniteseries #finitesums #infinitesums #oddsumformula #sumsofintegers #sums #shorts
To learn more about animating with manim, check out:
manim.community
"proofs without words"
*continues talking*
Just kidding, cool video :)
Hah! I do have an earlier version of this without any narration. A/B testing to see which gets more exposure :) Thanks!
Was thinking the same thing
Have to remember the mathematician Gauss who invented the proof for sum of n natural numbers when he's in school!! 😱🥶🧠
He didn't invent it, the story is that he discovered it on his own, obviously this was already known.
The story says that he calculated
S=1+2+3+...+100, by calculating
2S=(1+100)+(2+99)+...+(100+1)=10100,
so S=5050.
If you think about it, this may be a good general solution, but most children would solve it like this:
(1+99)+(2+98)+...+(49+51)+50+100
=4900+50+100=5050
I doubt the story is correct.
It's super easy to come up with tbh, Gauss should be remembered for his other mathematical feats
Gauss is greatest mathematician of all time
Remember He was 10 years old when he discovered it,
@@anonymous_FoXhe was 7
This channel is mega underrated … should blow up
Visual proofs with infinity are always kinda fishy. I wouldn’t rely on those. Other three are fantastic. Can you do one for summation of n^3 ?
I have seven sum of cubes visual proofs on the channel :)
Imma save this. This is art.
Beautiful!
1st equation I found them myself bc I wanted to shorten time to calculate infinite sums.
Then I've realized that wait if we cut a square in half & we add x cut in half again we get (x^2 +x)/2
The first and last one I figured out myself when facef with the series before when I was younger, but I never saw the middle two before, neat! Thanks!
You should do sum of cubes = square of sum of natural numbers
It’s on my channel many times. :)
Took me a minute, but I found it. Great video
Man i barely understand this right away but its cool
Awesome, mate ❤
* Awesome
@@robertveith6383 thamks 😂😂😂
तत्व बहुत अच्छा हैं Sirji
Mathologer has an awesome visual proof that ln is primitive of 1/x
wow so beautiful
1 is also an infinity. Some infinities are greater than others or at least represent a difference.
That's sooo cooool
It is awesome!!! How do you make it? Can you share me what tools you use?
I think it is manim
It is manim as noted.
Can I get the code?
Cool.
hell yeah
High five!!!!
😮 now I can die in peace😅
Isn't the last one (1/2)^n series? And that is a geometric series that would converge to 2
the series converges to 2 if you start at n=0 term, if you start at n=1 it converges to 1
You spoke
😊
I hope everyone watching this channel knows that these are used to make it easy to learn, but they are not actually sufficient as a proof. Pictures and diagrams are not proofs, if you use a diagram to explain, then it must be able to display all values of n for any positive integer n, unless you use induction
Can you make a visual proof for 1/n^2=pi^2/6
i think there's no way to fit it into a Short. 3blue1brown's video would better anyway (no offense, but he made manim!)
That is wrong/false. It is the *sum of* 1/n^2 from *n = 1 to oo* that equals [(pi)^2]/6.
Agree with this comment :)
Math is truly incredible
Hi there!
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