Mathematical Visual Proofs
Mathematical Visual Proofs
  • Видео 445
  • Просмотров 35 261 016

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Видео

Product of chords?Product of chords?
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 CompilationArithmetic Mean-Geometric Mean Visual Proof Compilation
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!Happy Tau Day!
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!Pythagorean theorem from a (semi) circle!
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)Sum Geometric Series with Ratio 1/2 in Rectangles (visual proofs)
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)0.66666… = 1 (in base 7)
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)A Factorial Sum Produces the Factorial Number System (visual proof)
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 SumAlternating Geometric Series Sum
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 TheodorusSpiral of Theodorus
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)Terdragon from the Chaos Game (visual fractal construction from iterated function system)
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 CalculusSum of a Positive Number and its Reciprocal from Calculus
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 ProofGarfield’s Pythagorean Proof
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)Root 2 is Irrational from Isosceles Triangle (visual proof)
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 SquaresSums of Fibonacci Squares
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 trianglesSum of positive number and its reciprocal from two triangles
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...

Комментарии

  • @laayiv9449
    @laayiv9449 3 часа назад

    Ive only clicked this video because the guy who invented it had a cool Greek name

  • @BadlyShipThatStillWorks
    @BadlyShipThatStillWorks 3 часа назад

    🍞

  • @lenrussell2424
    @lenrussell2424 3 часа назад

    Prob not, but I'm sure like to hunt down my compass and try!

  • @wsgk98
    @wsgk98 3 часа назад

    This shit looks like I'm gonna load it into my cap gun as a kid

  • @alanaralston
    @alanaralston 4 часа назад

    I do think so but I know I can pronounce Theodor correctly.

  • @Devon-2010
    @Devon-2010 4 часа назад

    Does anyone else see a tunnel to the infinite white void?

  • @DJDEADCATthelll
    @DJDEADCATthelll 5 часов назад

    do you think you can draw this by hand, NO I am not skilled enough

  • @SkyChu0
    @SkyChu0 5 часов назад

    Okay but like how do you get perpendicular?

  • @RPG_Guy-fx8ns
    @RPG_Guy-fx8ns 6 часов назад

    pi can equal anything if you are drunk enough.

  • @BaronSterling
    @BaronSterling 7 часов назад

    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.

  • @tiagobelo4965
    @tiagobelo4965 7 часов назад

    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.

  • @DreadEnder
    @DreadEnder 7 часов назад

    Maths and geometry are soo cool! And ammonitoidea to.

  • @sophiacristina
    @sophiacristina 8 часов назад

    Tau > Pi...

  • @Pantera1001
    @Pantera1001 8 часов назад

    you can use pi instead of tau as well as plus instead of minus minus

  • @anaestevez2130
    @anaestevez2130 8 часов назад

    I mean it really just looks like a seashell

  • @Leon-x5d
    @Leon-x5d 8 часов назад

    I love how the inside of the spiral is a growing ball of white hot stuff

  • @Grain979
    @Grain979 9 часов назад

    Isn't this just the fibbnotchi sequence, but just the spiral

  • @AJ_Sparten1337
    @AJ_Sparten1337 9 часов назад

    Looks like a snail shell.

  • @user-kp8ht1qo6r
    @user-kp8ht1qo6r 9 часов назад

    Spin from Jojos bizarre adventure

  • @mathiaskjeldgaardpetersen5926
    @mathiaskjeldgaardpetersen5926 9 часов назад

    e the pi while it's hot.

  • @user-yl8bu9qu7y
    @user-yl8bu9qu7y 10 часов назад

    Well, this is the best thing I've seen the whole day. Thank you for this amazing performance.❤

  • @Bluhbear
    @Bluhbear 10 часов назад

    The unnecessary circle step kinda pokes at my brain meat.

  • @leo-bf9dx
    @leo-bf9dx 11 часов назад

    i got both, Uzumaki and SBR vibes (moai emoji)

  • @wattwooson6829
    @wattwooson6829 11 часов назад

    The actual real sizes Mika - 10 inches Schlatt - 7 inches Astro and apandah are tied at 5.5 inches

  • @humongousfungusamongus3871
    @humongousfungusamongus3871 11 часов назад

    A nautilus... so to speak.

  • @mrvideo1115
    @mrvideo1115 11 часов назад

    2 ❌ √4✅

  • @ivanmax3595
    @ivanmax3595 12 часов назад

    ammonite gaming

  • @WootZoot
    @WootZoot 12 часов назад

    Cool

  • @gabrieletrovato3939
    @gabrieletrovato3939 12 часов назад

    I love it 👏🏻👏🏻

  • @Michelle6998832
    @Michelle6998832 12 часов назад

    Is this what they mean when they say: "You're spiraling out of control" ? 😂😂😂

  • @SinfulCreature
    @SinfulCreature 13 часов назад

    Source mappers will use this for elaborate stairwells

  • @31.DiepAnhTuan-bx4cg
    @31.DiepAnhTuan-bx4cg 13 часов назад

    I'm love it! I'm gonna learn this next 1 2 month at the 11 grade soon

  • @melinoanim
    @melinoanim 13 часов назад

    “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.

  • @musicofficial6924
    @musicofficial6924 14 часов назад

    By using infinity you can prove any number equal to any another number

  • @MONSTERGAMING-xv1hb
    @MONSTERGAMING-xv1hb 14 часов назад

    We got this is class 9 😅

  • @Turtlpwr
    @Turtlpwr 14 часов назад

    Math is so cool

  • @saildoth9183
    @saildoth9183 14 часов назад

    we got ourselves a nautilus

  • @LeetHaxington
    @LeetHaxington 14 часов назад

    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”

  • @samsonsoturian6013
    @samsonsoturian6013 15 часов назад

    Looks like a sea shell

  • @AmeyKalkotwarr
    @AmeyKalkotwarr 15 часов назад

    As an Indian, we learn this is class 9 maths as "Spiral Root"😅

  • @whatisahandle221
    @whatisahandle221 16 часов назад

    Cool!

  • @Frostlith
    @Frostlith 16 часов назад

    Bet

  • @user-nk8kb9pm4k
    @user-nk8kb9pm4k 16 часов назад

    something like it: x = middle section a = diameter of sphere or length of triangle side x=¼(a²•√3) - ½(π•(½a)²)

  • @TuxedoLion
    @TuxedoLion 16 часов назад

    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

  • @n8dawg640
    @n8dawg640 16 часов назад

    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

  • @sikdarkhalidmahmud7503
    @sikdarkhalidmahmud7503 16 часов назад

    No😂

  • @PerspectiveInsightReviews
    @PerspectiveInsightReviews 17 часов назад

    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!

  • @gladitsnotme
    @gladitsnotme 17 часов назад

    RUclips algorithm is broken af

  • @31.DiepAnhTuan-bx4cg
    @31.DiepAnhTuan-bx4cg 18 часов назад

    Good good thanks for the information brother

  • @mutafyanny
    @mutafyanny 18 часов назад

    Now do 0.111111111111111111111111111111111111111111111111111111111... = 1 (in base 2)