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Mathematical Visual Proofs
США
Добавлен 22 мар 2021
I animate and provide some explanation for classic and newer "proofs without words," which are typically diagrams without any words that indicate how a theorem could be proved.
I often pay homage to Proofs Without Words by including some animations without narration (only dramatic music :) ). I have also noticed that while there are many wonderful visual proofs available on RUclips, most of the creators do not credit the original visual proofs. I will do my best to include links and citations for each visual proof so that you can track down the original static images, which have a beauty and a wonder all their own.
I create my animations using the amazing software Manimgl from 3Blue1Brown.
If you want to buy me a coffee, you can do that here:
www.buymeacoffee.com/VisualProofs
I often pay homage to Proofs Without Words by including some animations without narration (only dramatic music :) ). I have also noticed that while there are many wonderful visual proofs available on RUclips, most of the creators do not credit the original visual proofs. I will do my best to include links and citations for each visual proof so that you can track down the original static images, which have a beauty and a wonder all their own.
I create my animations using the amazing software Manimgl from 3Blue1Brown.
If you want to buy me a coffee, you can do that here:
www.buymeacoffee.com/VisualProofs
Видео
Product of chords?
Просмотров 11 тыс.5 дней назад
This short animation shows chords connecting n equally space points to one of those points on a unit circle and computes the product of the chord lengths. Do you have a conjecture based on this? Can you prove it? If you’re interested, check out the related video at ruclips.net/video/OedLfHaj2p4/видео.htmlsi=VFiIFOmeDCWgGBYF . This animation is based on a famous problem that has been discussed i...
Arithmetic Mean-Geometric Mean Visual Proof Compilation
Просмотров 4,1 тыс.6 дней назад
This video is a compilation of seven shorter videos that I have created showing various visual proofs without words of the famous AM-GM inequality, which states that the arithmetic mean of two numbers (a b)/2 is greater than or equal to the geometric mean of the two numbers square root of a times b. To see the original videos (in shorter form and sometimes with words/explanations), check the li...
Happy Tau Day!
Просмотров 24 тыс.9 дней назад
In this short video, we show one way to visualize the constant tau, which is twice pi, as the area between the curves 1/(1 x^2) and its negation over the entire real line. Happy Tau Day if you celebrate! To buy me a coffee, head over to www.buymeacoffee.com/VisualProofs Thanks! #mathshorts #mathvideo #math #short #math #manim #radian #circle #radius #tauday #taurus #calculus To learn more about...
Pythagorean theorem from a (semi) circle!
Просмотров 35 тыс.12 дней назад
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the semicircle and Thales triangle theorem. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. This animation is based on a proof due to Michael Hardy from the November, 1986 issue of The College Math Journal (doi.or...
Sum Geometric Series with Ratio 1/2 in Rectangles (visual proofs)
Просмотров 3,5 тыс.14 дней назад
In this video, we show an animated version of a recent proof without words that finds the sum of the geometric series with first term 1/root(2) 1/2 and ratio 1/2 using the unit square. Then we show how to find other geometric series sums with ratio 1/2 using different sizes of rectangles. Careful, the final bonus question might require a different technique than rotating :) If you like this vid...
0.66666… = 1 (in base 7)
Просмотров 99 тыс.19 дней назад
This is a short, animated visual proof showing the sum of the infinite geometric series with first term 6/7 and ratio 1/7, which in turn allows us to compute the sum of the series of powers of 1/7 and determine an interesting base 7 representation of 1. If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualProofs. Thanks! For a lo...
A Factorial Sum Produces the Factorial Number System (visual proof)
Просмотров 10 тыс.21 день назад
This is a short, animated visual proof demonstrating a finite sum involving products of factorials. The proof exploits the classic inductive proof of the formula in question. As a bonus, we discuss the factorial number system and show how the formula can be used to count up in this system. If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoff...
Alternating Geometric Series Sum
Просмотров 74 тыс.23 дня назад
This is a short, animated visual proof demonstrating the infinite alternating geometric series formula for any positive ratio r with r less than 1 and with positive first term a. This series is important for many results in calculus, discrete mathematics, and combinatorics. To buy me a coffee, head over to www.buymeacoffee.com/VisualProofs Thanks! For a slower, wide format version of this video...
Spiral of Theodorus
Просмотров 433 тыс.26 дней назад
This is a short, animated visual proof demonstrating how to construct square roots of any positive integer using the Spiral of Theodorus To buy me a coffee, head over to www.buymeacoffee.com/VisualProofs Thanks! #manim #math #mathshorts #mathvideo #construction #geometry #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #spiral #theodorus #squ...
Terdragon from the Chaos Game (visual fractal construction from iterated function system)
Просмотров 2,3 тыс.28 дней назад
In this video, we show how to use a random process of iteratively applying three affine transformations in the real plane to generate a 3-rep-tile known as the Terragon. What happens if you do something similar with different affine linear transformations? Check out these videos for related constructions: ruclips.net/video/rLxx6b-oJGo/видео.html ruclips.net/video/NBI_5GdvqUo/видео.html ruclips....
Sum of a Positive Number and its Reciprocal from Calculus
Просмотров 55 тыс.Месяц назад
This is a short, animated visual proof demonstrating that sum of a positive real number and its reciprocal is always greater than or equal to 2. To buy me a coffee, head over to www.buymeacoffee.com/VisualProofs Thanks! It turns out that this theorem is equivalent to the Arithmetic Mean-Geometric Mean inequality. The equivalence is implied by the following two proofs: ruclips.net/video/62G9fak1...
Garfield’s Pythagorean Proof
Просмотров 74 тыс.Месяц назад
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the trapezoid that is now attributed to President James Garfield. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. To buy me a coffee, head over to www.buymeacoffee.com/VisualProofs Thanks! This animation is based ...
Root 2 is Irrational from Isosceles Triangle (visual proof)
Просмотров 20 тыс.Месяц назад
In this short, we use a famous argument by Tom Apostol to prove that the square root of two is irrational by infinite descent using a right isosceles triangle. We also go a bit further and show how this proof hints at the number theoretic construction of the convergents of the square root of two, which are the best rational approximations of root 2. If you like this video, consider subscribing ...
Sums of Fibonacci Squares
Просмотров 39 тыс.Месяц назад
This is a short, animated visual proof demonstrating the sum of the squares of the first n consecutive Fibonacci numbers. To buy me a coffee, head over to www.buymeacoffee.com/VisualProofs Thanks! To see a slower, wider high definition version of this visual identity (without words), check out this video: ruclips.net/video/2EsoiBdnIAM/видео.htmlsi=3bW8M_zxxx-ueAhC Also, check out my playlist on...
Sum of positive number and its reciprocal from two triangles
Просмотров 23 тыс.Месяц назад
This is a short, animated visual proof demonstrating that sum of a positive real number and its reciprocal is always greater than or equal to 2. To buy me a coffee, head over to www.buymeacoffee.com/VisualProofs Thanks! For a wider format and slightly longer version of this proof, see ruclips.net/video/BkQvnriVblY/видео.htmlsi=cldTUiQAtPuZLvto It turns out that this theorem is equivalent to the...
Ive only clicked this video because the guy who invented it had a cool Greek name
🍞
Prob not, but I'm sure like to hunt down my compass and try!
This shit looks like I'm gonna load it into my cap gun as a kid
I do think so but I know I can pronounce Theodor correctly.
Does anyone else see a tunnel to the infinite white void?
do you think you can draw this by hand, NO I am not skilled enough
Okay but like how do you get perpendicular?
pi can equal anything if you are drunk enough.
Well, two minutes into the video and already the objectively incorrect take of "Heavy Blade is really bad" has appeared. Not giving me confidence in the rest of this video.
I'd probably do something like a 14x2 triangle 14^2+2^2=196+4=200, since the hypothenuse is the square root of the sum of the squares the resulting hypothenuse would have a length of sqrt(200), now if you asked me to draw it intersecting two specified points I'd just give up.
Maths and geometry are soo cool! And ammonitoidea to.
Tau > Pi...
you can use pi instead of tau as well as plus instead of minus minus
No, you can't do either
I mean it really just looks like a seashell
I love how the inside of the spiral is a growing ball of white hot stuff
Isn't this just the fibbnotchi sequence, but just the spiral
Looks like a snail shell.
Spin from Jojos bizarre adventure
e the pi while it's hot.
Well, this is the best thing I've seen the whole day. Thank you for this amazing performance.❤
The unnecessary circle step kinda pokes at my brain meat.
i got both, Uzumaki and SBR vibes (moai emoji)
The actual real sizes Mika - 10 inches Schlatt - 7 inches Astro and apandah are tied at 5.5 inches
A nautilus... so to speak.
2 ❌ √4✅
ammonite gaming
Cool
I love it 👏🏻👏🏻
Is this what they mean when they say: "You're spiraling out of control" ? 😂😂😂
Source mappers will use this for elaborate stairwells
I'm love it! I'm gonna learn this next 1 2 month at the 11 grade soon
“Do you think you could construct this by hand?” Do I have the dedication: no Do I have the patience: no Do I have the time: yes - In short no.
By using infinity you can prove any number equal to any another number
We got this is class 9 😅
Math is so cool
we got ourselves a nautilus
Everybody’s out there trying to calculate the moon landing and figure out how to calculate pi stuff. Theo is sitting in the corner with crayons “HEY GUY LOOK AT MY SPIRAL. IM GONNA NAME THIS AFTER MYSELF DURRRR THE BEST PART ABOUT ADVANCING SCIENCE AND MATH IS THE PERSONAL GLORY OF HAVING MY CONFUSING NAME BE PART OF A THING PEOPLE HAVE TO LEARN DURRRR LOL” Everyone stops and looks at him. “HEY EINSTEIN. I GUESS WE’RE BOTH EQUALLY RECOGNIZED MATH CONTRIBUTORS. ISN’T THAT FUNNY? LOL”
Looks like a sea shell
As an Indian, we learn this is class 9 maths as "Spiral Root"😅
Cool!
Bet
something like it: x = middle section a = diameter of sphere or length of triangle side x=¼(a²•√3) - ½(π•(½a)²)
not sure i see the purpose of drawing the circle? since the next line you draw is always of length 1 and always perpendicular 🤔 what am i not getting
You don’t even need to construct the circle, you just are making right triangles with sides of 1 and whatever square root length the previous triangle’s hypotenuse is
No😂
Wow. That was a movie. This is some of the best content on youtube Ive ever seen. It was so interesting and exciting to follow you along on this adventure, and it really makes me want to do something like this myself. And I probably will. I have actually been in that exact mine once, so it was cool to see it again and also see more of it. Absolutely amazing video, I will definitely subscribe!
RUclips algorithm is broken af
Good good thanks for the information brother
Now do 0.111111111111111111111111111111111111111111111111111111111... = 1 (in base 2)
It’s on the channel… 😀