Mathologer
Mathologer
  • Видео 103
  • Просмотров 70 709 149
Conway's IRIS and the windscreen wiper theorem
Conway's whatever ... it's named after John Conway and so it must be good :)
Wiki page dedicated to John Conway
en.wikipedia.org/wiki/John_Horton_Conway
Wiki page Conway's circle
en.wikipedia.org/wiki/Conway_circle_theorem
Wiki page on his Game of Life
en.wikipedia.org/wiki/Conway%27s_Game_of_Life
Michael de Villiers (the connection with the windscreen wiper theorem, read this one first)
dynamicmathematicslearning.com/conway-circle-theorem-special-case-side-divider-theorem.pdf
dynamicmathematicslearning.com/conway-circle-as-special-side-divider-theorem.html
Also check out Michael's main page dynamicmathematicslearning.com/homepage4.html
Matt Baker's tribute blog to John Conway
mattbaker.blog/2020/04...
Просмотров: 70 584

Видео

Simple yet 5000 years missed ?
Просмотров 199 тыс.2 месяца назад
Good news! You really can still discover new beautiful maths without being a PhD mathematician. Stumbled across this one while working on the magic squares video. Another curious discovery by recreational mathematician Lee Sallows. A simple and beautiful and curious fact about triangles that, it appears, was first discovered only 10 years ago. Really quite amazing that this one got overlooked, ...
What's the curse of the Schwarz lantern?
Просмотров 166 тыс.4 месяца назад
Second coop with Andrew. This time it's about the Schwarz lantern a very famous counterexample to something that mathematicians believed to be obviously true. A 3D cousin of the famous pi = 4 paradox. 00:00 Intro 00:39 Troll math: the pi=4 meme 02:25 Archimedes chops off corners 05:51 Archimedes boxing of pi 07:40 Schwarz lantern 16:59 Area formula 17:12 Schwarz pi = 4 memes 20:17 Folding flat ...
Why are the formulas for the sphere so weird? (major upgrade of Archimedes' greatest discoveries)
Просмотров 203 тыс.5 месяцев назад
In today’s video we’ll make a little bit of mathematical history. I'll tell you about a major upgrade of one of Archimedes' greatest discoveries about the good old sphere that so far only a handful of mathematicians know about. 00:00 Intro to the baggage carousel 01:04 Archimedes baggage carousel 04:26 Inside-out animations 04:59 Inside-out discussion 10:38 Inside-out paraboloid 12:43 Ratio 3:2...
Is this a paradox? (the best way of resolving the painter paradox)
Просмотров 107 тыс.6 месяцев назад
The painter's paradox, a.k.a. Gabriel's horn paradox a.k.a. Torricelli's horn paradox has been done to death on RUclips. So why do it again? Well, being all about some remarkable features of 1/x, this topic nicely complements the previous two videos that were also dedicated to 1/x. Now the first Mathologer trilogy is complete! Also, I thought of a couple of nice twists to make this treatment of...
The best A - A ≠ 0 paradox
Просмотров 384 тыс.7 месяцев назад
This video is about a new stunning visual resolution of a very pretty and important paradox that I stumbled across while I was preparing the last video on logarithms. 00:00 Intro 00:56 Paradox 03:52 Visual sum = ln(2) 07:58 Pi 11:00 Gelfond's number 14:22 Pi exactly 17:35 Riemann's rearrangement theorem 22:40 Thanks! Riemann rearrangement theorem. en.wikipedia.org/wiki/Riemann_series_theorem Th...
Why don't they teach simple visual logarithms (and hyperbolic trig)?
Просмотров 339 тыс.8 месяцев назад
Simple visual logarithms. Is there such a thing? You bet :) 00:00 Intro 01:59 Rubik's cube and drill 03:26 What's the area? 05:15 Sum of 1 1/2 1/3 ... 06:35 Mystery sum 11:32 What base? 17:25 What is Log_b(x)? 22:14 Is this a circle? 28:53 Proof that e^a = cosh(a) sinh(a) 30:50 Thanks Maths of spinning cubes by Lingguo Bu tinyurl.com/yvp5udm6 Great history of hyperbolic functions by Janet Heine...
Ramanujan's easiest hard infinity monster (Mathologer Masterclass)
Просмотров 157 тыс.10 месяцев назад
In this masterclass video we'll dive into the mind of the mathematical genius Srinivasa Ramanujan. The focus will be on rediscovering one of his most beautiful identities. 00:00 Intro 02:48 How did his mind work? 09:12 What IS this? 15:11 Fantastic fraction 18:12 Impossible identity 23:38 Thanks! This video was inspired by two 2020 blog posts by John Baez: math.ucr.edu/home/baez/ramanujan/ Here...
Powell’s Pi Paradox: the genius 14th century Indian solution
Просмотров 491 тыс.11 месяцев назад
Around 1400 there lived an Indian astronomer and mathematician by the name of Madhava of Saṅgamagrāma. He was the greatest mathematician of his time and, among other mathematical feats, he and his followers managed to discover a lot of calculus 200 years before Newton and Leibniz did their thing. While preparing a video about this Indian calculus it occurred to me that some of Madhava's discov...
The Korean king's magic square: a brilliant algorithm in a k-drama (plus geomagic squares)
Просмотров 126 тыс.Год назад
A double feature on magic squares featuring Bachet's algorithm embedded in the Korean historical drama series Tree with deep roots and the Lee Sallow's geomagic squares. 00:00 Intro 02:52 Part 1: The king's magic squares 09:40 Proof 18:22 The order 5 and 7 magic squares 19:17 Part 2: Geometric magic square 30:59 Thanks! The Korean historical drama Tree with deep roots is available here www.viki...
What's hiding beneath? Animating a mathemagical gem
Просмотров 146 тыс.Год назад
There is a lot more to the pretty equation 10² 11² 12² = 13² 14² than meets the eye. Let me show you. 00:00 Intro 00:07 Animated visual proofs 03:35 Mathologer materializes 06:31 Three puzzles 07:45 Thanks! Notes: The beautiful visual proof for the squares pattern is based on a note by Michael Boardman in Mathematics Magazine: tinyurl.com/2d4y7wtf As far as I can tell, I am the first one to not...
Fibonacci = Pythagoras: Help save a beautiful discovery from oblivion
Просмотров 241 тыс.Год назад
In 2007 a simple beautiful connection Pythagorean triples and the Fibonacci sequence was discovered. This video is about popularising this connection which previously went largely unnoticed. 00:00 Intro 07:07 Pythagorean triple tree 13:44 Pythagoras's other tree 16:02 Feuerbach miracle 24:28 Life lesson 26:10 The families of Plato, Fermat and Pythagoras 30:45 Euclid's Elements and some proofs 3...
Pythagoras twisted squares: Why did they not teach you any of this in school?
Просмотров 452 тыс.Год назад
A video on the iconic twisted squares diagram that many math(s) lovers have been familiar with since primary school. Surprisingly, there is a LOT more to this diagram than even expert mathematicians are aware of. And lots of this LOT is really really beautiful and important. A couple of things covered in this video include: Fermat's four squares theorem, Pythagoras for 60- and 120-degree triang...
Secrets of the lost number walls
Просмотров 162 тыс.Год назад
This video is about number walls a very beautiful corner of mathematics that hardly anybody seems to be aware of. Time for a thorough Mathologerization :) Overall a very natural follow-on to the very popular video on difference tables from a couple of months ago ("Why don't they teach Newton's calculus of 'What comes next?'") 00:00 Intro 01:02 Chapter 1: What's in a wall 03:35 Chapter 2: Number...
Why is calculus so ... EASY ?
Просмотров 1,5 млнГод назад
Calculus made easy, the Mathologer way :) 00:00 Intro 00:49 Calculus made easy. Silvanus P. Thompson comes alive 03:12 Part 1: Car calculus 12:05 Part 2: Differential calculus, elementary functions 19:08 Part 3: Integral calculus 27:21 Part 4: Leibniz magic notation 30:02 Animations: product rule 31:43 quotient rule 32:18 powers of x 33:10 sum rule 33:52 chain rule 34:54 exponential functions 3...
Heron’s formula: What is the hidden meaning of 1 + 2 + 3 = 1 x 2 x 3 ?
Просмотров 502 тыс.Год назад
Heron’s formula: What is the hidden meaning of 1 2 3 = 1 x 2 x 3 ?
Reinventing the magic log wheel: How was this missed for 400 years?
Просмотров 369 тыс.2 года назад
Reinventing the magic log wheel: How was this missed for 400 years?
Tesla’s 3-6-9 and Vortex Math: Is this really the key to the universe?
Просмотров 3,9 млн2 года назад
Tesla’s 3-6-9 and Vortex Math: Is this really the key to the universe?
How did Fibonacci beat the Solitaire army?
Просмотров 172 тыс.2 года назад
How did Fibonacci beat the Solitaire army?
The 3-4-7 miracle. Why is this one not super famous?
Просмотров 580 тыс.2 года назад
The 3-4-7 miracle. Why is this one not super famous?
Do you understand this viral very good math movie clip? (Nathan solves math problem X+Y)
Просмотров 692 тыс.2 года назад
Do you understand this viral very good math movie clip? (Nathan solves math problem X Y)
Why don't they teach Newton's calculus of 'What comes next?'
Просмотров 807 тыс.2 года назад
Why don't they teach Newton's calculus of 'What comes next?'
The Iron Man hyperspace formula really works (hypercube visualising, Euler's n-D polyhedron formula)
Просмотров 303 тыс.2 года назад
The Iron Man hyperspace formula really works (hypercube visualising, Euler's n-D polyhedron formula)
The Moessner Miracle. Why wasn't this discovered for over 2000 years?
Просмотров 685 тыс.2 года назад
The Moessner Miracle. Why wasn't this discovered for over 2000 years?
The Pigeon Hole Principle: 7 gorgeous proofs
Просмотров 180 тыс.3 года назад
The Pigeon Hole Principle: 7 gorgeous proofs
The ultimate tower of Hanoi algorithm
Просмотров 222 тыс.3 года назад
The ultimate tower of Hanoi algorithm
Explaining the bizarre pattern in making change for a googol dollars (infinite generating functions)
Просмотров 141 тыс.3 года назад
Explaining the bizarre pattern in making change for a googol dollars (infinite generating functions)
The ARCTIC CIRCLE THEOREM or Why do physicists play dominoes?
Просмотров 323 тыс.3 года назад
The ARCTIC CIRCLE THEOREM or Why do physicists play dominoes?
700 years of secrets of the Sum of Sums (paradoxical harmonic series)
Просмотров 777 тыс.3 года назад
700 years of secrets of the Sum of Sums (paradoxical harmonic series)
The hardest "What comes next?" (Euler's pentagonal formula)
Просмотров 744 тыс.3 года назад
The hardest "What comes next?" (Euler's pentagonal formula)

Комментарии

  • @w.flores8868
    @w.flores8868 19 часов назад

    This is so basic

  • @w.flores8868
    @w.flores8868 19 часов назад

    Who fuckin cares. You guys are making more complicated than what it is. You guys are just bored and make yourself look smarter. This could have been done along time ago. Nothing new sir.

  • @filmfilms827
    @filmfilms827 День назад

    thank you, best explanation because it actually explains why, which i think is the most important to understanding

  • @joinfortherapy6470
    @joinfortherapy6470 День назад

    Top 5 in the math olympiad class that is a grade above me, somehow struggles with sequences and complex patterns

  • @soundsoflife9549
    @soundsoflife9549 День назад

    You have to have a row of 49 circles then trick the geometry.

  • @Armyvet12
    @Armyvet12 День назад

    If multiplications concept is to increase in number... how does 0's and 1's follow the concept of multiplication? Lol

  • @abhishekk3022
    @abhishekk3022 День назад

    Rare ,, one in a billion !

  • @nin10dorox
    @nin10dorox День назад

    I'm pausing to try to prove it, and I think I got it! It's hard to explain without pictures, but the incircle meets each side of the triangle, splitting each into two segments. We can say red=a+b, blue=b+c, and green=c+a. The line extended from the red side has a length of a+blue = a+b+c below its tangent point to the incircle. And it has a length of b+green = b+c+a above the tangent point. So it is tangent to the incircle at its midpoint. The same goes for the other two extended lines. Since each line is the same length, and they're all balancing on the incircle at their midpoints, they are the same thing, just rotated around the incircle's center. Thus their endpoints all lie on a circle.

    • @nin10dorox
      @nin10dorox День назад

      I came up with the color proof, but man that swivel proof was slick!

  • @TheRMeerkerk
    @TheRMeerkerk 2 дня назад

    Are there pairs of sequences in each box?

    • @TheRMeerkerk
      @TheRMeerkerk 2 дня назад

      No, because if you take from two sequences from two different boxes, then they should not be close.

    • @TheRMeerkerk
      @TheRMeerkerk День назад

      This is actually hurting my brain and I've already seen a lot of infinity related stuff. So when you look inside a single box, you can't say that they have even a single bit all in common, but they are all close? The first bit can't be the same for all, because both 1X and 0X (X is an infinite sequence concatenated to the bit in front of it) are close and should therefore be in the same box. In fact for any finite sequence Y and infinite sequence X we know that Y1X and Y0X are both in the same box. Even any YX and ZX are in same box as long as Y and Z are sequences with the same finite length. But there is no limit on how much two sequences can differ. So Y and Z can be complete opposites and googolplex long and that still would mean that YX and ZX go in the same box.

  • @eonasjohn
    @eonasjohn 2 дня назад

    Thank you for the video.

  • @areuokay4984
    @areuokay4984 2 дня назад

    Goodluck if you get it you get it if not bye

  • @eonasjohn
    @eonasjohn 2 дня назад

    Thank you for the video.

  • @mahuma4168
    @mahuma4168 2 дня назад

    14:20 mistake detected boss "

  • @wyattstevens8574
    @wyattstevens8574 2 дня назад

    So for the broken cross rule for windows n>1, is it always (I'll use A B C D for the 3-term blocks) A-B=C-D, or does it change with the value of n?

  • @thomaswipf7986
    @thomaswipf7986 2 дня назад

    Did I miss this in gradeschool/college? I only took basic maths to get my CPA.

  • @markwrede8878
    @markwrede8878 3 дня назад

    "Choice" is not a rigorously defined math activity.

  • @kates347
    @kates347 3 дня назад

    Where can I message you personally? I have interesting findings with numbers.

  • @RealPackCat
    @RealPackCat 3 дня назад

    I wonder if women only see the numbers, and men see the visual patterns?

  • @storypals
    @storypals 3 дня назад

    Spectacular! Wow, the best math teach ever!

  • @someguy303-hz5yz
    @someguy303-hz5yz 3 дня назад

    my ex girlfriend has a masters in matth i think she is an alien

  • @AshitBaranKanjilal
    @AshitBaranKanjilal 3 дня назад

    Both proofs have their own path of application. A great discovery!!

  • @Gru39
    @Gru39 3 дня назад

    The bright white background is putting off

  • @holgerjrgensen2166
    @holgerjrgensen2166 4 дня назад

    It is all about Form and Volume, different forms same volume, or doubble volume, in same form.

  • @holgerjrgensen2166
    @holgerjrgensen2166 4 дня назад

    Your starter-psychosis, is a starter-psychosis, there is No need of 'ok' and starter everything, it is animal instinct sounds, just a phychosis. (Not Mathematic) the Heart of Mathematic is Perspective + Logic and Order = Mathematic. Time is the 'shadow' of Motion.

  • @snneakydevil
    @snneakydevil 4 дня назад

    best combo in the era of gaming??? ?

  • @holgerjrgensen2166
    @holgerjrgensen2166 4 дня назад

    Turn a clay-cube, into a ball.

  • @VioletGiraffe
    @VioletGiraffe 4 дня назад

    I like the coloring proof by far, the swivel proof didn't feel like it even proves anything, but a very interesting fact.

  • @NareLusinyan
    @NareLusinyan 5 дней назад

    Մոռանում ես,որ' ՀԱՅ էր,Հային ՀԱՅՈՒԹՅՈՒՆ չես սովորեցնի,ՆԱ' ՍՈՎՈՐՎԱԾ է ԾՆՎՈՒՄ😂❤+**12

  • @user-qe1vz3qw1x
    @user-qe1vz3qw1x 5 дней назад

    "you did not steal from me. You stole me from mankind" - Tesla

  • @LheannMichelleFlorento-xc7ux
    @LheannMichelleFlorento-xc7ux 5 дней назад

    I feel like calculus is hard but when you know them its like doing 1+1

  • @jjnevis
    @jjnevis 5 дней назад

    It's only half the story, if you want to see the rest, try this: e^(iTau)=1

  • @joaofrutinho
    @joaofrutinho 5 дней назад

    The only thing I don't understand is way you use 10 M instead of any other number. Could someone explain the reason for this?

    • @johnlabonte-ch5ul
      @johnlabonte-ch5ul 3 дня назад

      Using times 10 is the best way to provide the cancelation of the infinite decimal through a circular algorithm; Times 10 Subtract 1 Divide by 9 Notice it doesn't work if; Times 10 Add 1 Divide by 11.

    • @Chris-5318
      @Chris-5318 3 дня назад

      @@johnlabonte-ch5ul KarenTheBonehead, what is this circular algorithm that you keep on blathering about? I'll translate your word based procedures into normal arithmetic: Times 10: 10 * 0.999... = 9.999... Subtract 1: 9.999... - 1 = 8.999... Divide by 9: 8.999... / 9 = 0.999... "Notice it doesn't work if;" ??? (see below). Times 10: 10 * 0.999... = 9.999... Add 1: 9.999... + 1 = 10.999... Divide by 11: 10.999... / 11 = 0.999... What doesn't work? As usual, you just mutter some junk and don't explain or illustrate what you mean. I have no idea what you were trying to prove with either of your weird procedures. None of it in any way invalidates Mathologer's proof or that 0.999... = 1. There is something seriously wrong with your cognition. You need to get an MRI scan done.

    • @Chris-5318
      @Chris-5318 3 дня назад

      ​@@johnlabonte-ch5ul Karen, I forgot to say that there is nothing special about using 10, other than it makes the arithmetic simpler (as it is equivalent to shifting the decimal place one place to the right). Let's try 7 instead of 10, and also go back to a sensible procedure: 7 * 0.999... = 6.999... => 6 * 0.999... + 0.999... = 6 + 0.999... => 6 * 0.999... = 6 => 0.999... = 6/6 = 1 You have been told that sort of thing several times, by me. Because I know the sort of fallacious objection that you'll make, I'll prove that 7 * 0.999... = 6.999... 7 * 0.999... = 7 * (0.9 + 0.09 + 0.009 + ...) = 7 * 0.9 + 7 + 0.09 + 7 + 0.009 + ... = 6.3 + 0.63 + 0.063 + ... = (6 + 0.3) + (0.6 + 0.03) + (0.06 + 0.003) + .... = 6 + (0.3 + 0.6) + (0.03 + 0.06) + (0.003 + 0.006) + ... = 6 + 0.9 + 0.09 + 0.009 + ... = 6.999... In case I haven't said it recently, you are a muppet, and you need to get an MRI scan to find a possible explanation for that, your serious loss of memory and your lack of cognition and comprehension.

  • @jbruuuu
    @jbruuuu 5 дней назад

    Why is it that the numerator in the continued fraction for 2 is never replaced with the identity 2 / (3 - 2)?

  • @quantumgaming9180
    @quantumgaming9180 6 дней назад

    At 21:10, why is obvious that any 2 cycles have the same length? I know we can prove this with Lagrange's theorem for groups but is there an easier explanation that I am missing?

  • @johnlabonte-ch5ul
    @johnlabonte-ch5ul 6 дней назад

    The basic question is 0<nx where n is a real number and x is (Lim of ".99..."=1) minus ".99..." Stated differently is the limit of ".99..." the same as ".99..." I say no. ".99..." is equivalent to 1 not exactly equal. 1/3 is equivalent to ".33..." not exactly equal. 0<n((lim n->°° ".33..." =1/3) minus ".33...") and 1 divided by 3 is not complete.

    • @johnlabonte-ch5ul
      @johnlabonte-ch5ul 6 дней назад

      Any infinitely repeating decimal is incomplete and imprecise.

    • @Chris-5318
      @Chris-5318 5 дней назад

      ​@@johnlabonte-ch5ul For the zillionth time, what does ' Lim of ".99..." ' mean? Specifically, what is x and y for lim x->y 0.999... and how does either x or y have anything to do with 0.999...? I'm still WAAAAAAIIIIITINGTINGTING... Duh! If 0.999... doesn't equal 1 exactly, then it cannot be equivalent to 1. You just keep on repeating the same nonsensical gibberish over and over again, only have it shot down over and over again. You then run away for a few days, then repeat the cycle by starting a new thread. You have a serious problem. You really need to get an MRI scan.

    • @Chris_5318
      @Chris_5318 5 дней назад

      @@johnlabonte-ch5ul You: "Any infinitely repeating decimal is incomplete and imprecise." Where's your proof? The fact is that all decimals are complete and precise. If you claim that 0.999... is only approximately 1, then what is 1 - 0.999... and give a proof?

    • @johnlabonte-ch5ul
      @johnlabonte-ch5ul 5 дней назад

      Infinity is incomplete, inconsistent and imprecise.

    • @Chris_5318
      @Chris_5318 5 дней назад

      @@johnlabonte-ch5ul You claims are incomplete, inconsistent and imprecise nonsense. Explain and prove what you mean.

  • @mtgatutorials368
    @mtgatutorials368 6 дней назад

    I want to know what it would look like if you took this 2 dimensional diagram and formula and created the 3D equivalent !!! What would that look like? We want to know !!!

  • @Findmylimit
    @Findmylimit 6 дней назад

    I think I’m going to teach myself calculus

  • @donwald3436
    @donwald3436 7 дней назад

    Your shirt is too distracting 😂😂😂

  • @3Max
    @3Max 7 дней назад

    I'm getting a little lost on the whole reordering business (how do we re-order the CupDdown permutation to the shift permutation?). I get (or trust really) that you're allowed to reorder it, but i'm not seeing exactly HOW you're reordering it. Will need to watch again closely!

  • @Mochii_icecream
    @Mochii_icecream 7 дней назад

    Flipping the egde while srcambling part of the cube was pretty easy... Hint: Use M and U moves

  • @RichardKandarian
    @RichardKandarian 7 дней назад

    Compare turning something inside out versus reflecting it across it's surface.

  • @3Max
    @3Max 7 дней назад

    "Don't worry if you don't get every detail in the FIRST viewing" -- do you really think I'm going to watch this 10 times? Well, you're exactly right.

  • @SixballQ45
    @SixballQ45 8 дней назад

    All multiples of 3 add up to 3, 6, or 9 - its not unique to JUST 9

  • @johannestan8681
    @johannestan8681 8 дней назад

    Please help. I don't understand why to cube uv then multiply u^3+v^3 by v^3. Looks like the equation will become unbalance

  • @EinSmileyZuViel
    @EinSmileyZuViel 8 дней назад

    I guess the coupon is worth $10 x (18/37)

  • @pauselab5569
    @pauselab5569 8 дней назад

    It flips front and behind. The reason why we think it flips left and right is that we are so used to turning to see behind our backs instead of doing a backflip or something. In fact you have probably understood what I meant by turning to see behind without me ever mentioning that it was with respect to the z axis. It might have been the x axis but it’s so unusual that we don’t think about it.

  • @mehmeteminconkar2590
    @mehmeteminconkar2590 8 дней назад

    Bro u are on the voices english book a2 level in topic 10c page 2 listening take a look

  • @ivandrian2
    @ivandrian2 9 дней назад

    I am wondering if our conclusion about particular number "properties" comes from arbitrary choice of Numeral System base? "9" has significance only if we use 10-base system. I guess it would be "F" in hex-base, "7" for octal-base. For binary system all will jam to "1".

  • @jurgenblick5491
    @jurgenblick5491 9 дней назад

    Brilliant

  • @Robloxan899
    @Robloxan899 9 дней назад

    HEW! INF/INF!!!! 😂❤❤😂❤😂❤😂😂❤