Mathologer
Mathologer
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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/2020/04/15/some-mathematical-gems-from-john-conway/#more-4162
Tanya Khovanova's blog post on Conway's circle showing Conway's wearing a Conway circled Mathcamp t-shirt
blog.tanyakhovanova.com/2010/06/conways-circle/
Colin Beveridge's proof without words
aperiodical.com/2020/05/the-big-lock-down-math-off-match-14/
Colin Beveridge and Elizabeth A Wilson (his proof without words explained :)
aperiodical.com/2020/06/conways-circle-theorem-a-proof-this-time-with-words/
Paul Farrel's beautiful animated proof
ua-cam.com/video/MvLBeOIPZ08/v-deo.html
Me on Conway's circle and Conway's pinwheel tiling for the Gathering of Gardner
ua-cam.com/video/VrXnwmyxylg/v-deo.html
Card Colm on Conway and his circle
www.cardcolm.org/JHC.html
cardcolm.org/Pics/RybaConwayCircle.pdf
Eric Braude
Conways Circle Theorem: A Short Proof Enabling Generalization to Polygons
arxiv.org/abs/2111.01835
Mathologer video on curves of constant width
New Reuleaux Triangle Magic
ua-cam.com/video/-eQaF6OmWKw/v-deo.html
Mathologer videos on Conway's proof of Morley's miracle
Math is Illuminati confirmed
ua-cam.com/video/DfnBW6HvNwM/v-deo.html
Part 2
ua-cam.com/video/gjhmh3yWiTI/v-deo.html
Music: Rain by ANBR and Ethereal Ottom
T-shirt: ages old, don't remember where I got this one from
Enjoy!
Burkard
Переглядів: 69 845

Відео

Simple yet 5000 years missed ?
Переглядів 199 тис.2 місяці тому
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?
Переглядів 166 тис.4 місяці тому
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)
Переглядів 202 тис.5 місяців тому
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)
Переглядів 107 тис.6 місяців тому
The painter's paradox, a.k.a. Gabriel's horn paradox a.k.a. Torricelli's horn paradox has been done to death on UA-cam. 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
Переглядів 384 тис.7 місяців тому
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)?
Переглядів 338 тис.8 місяців тому
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)
Переглядів 157 тис.10 місяців тому
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
Переглядів 491 тис.11 місяців тому
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)
Переглядів 126 тис.Рік тому
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
Переглядів 146 тис.Рік тому
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
Переглядів 240 тис.Рік тому
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?
Переглядів 452 тис.Рік тому
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
Переглядів 162 тис.Рік тому
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 ?
Переглядів 1,5 млнРік тому
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 ?
Переглядів 502 тис.Рік тому
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?
Переглядів 368 тис.2 роки тому
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?
Переглядів 3,9 млн2 роки тому
Tesla’s 3-6-9 and Vortex Math: Is this really the key to the universe?
How did Fibonacci beat the Solitaire army?
Переглядів 172 тис.2 роки тому
How did Fibonacci beat the Solitaire army?
The 3-4-7 miracle. Why is this one not super famous?
Переглядів 580 тис.2 роки тому
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)
Переглядів 691 тис.2 роки тому
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?'
Переглядів 806 тис.2 роки тому
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)
Переглядів 303 тис.2 роки тому
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?
Переглядів 685 тис.2 роки тому
The Moessner Miracle. Why wasn't this discovered for over 2000 years?
The Pigeon Hole Principle: 7 gorgeous proofs
Переглядів 180 тис.3 роки тому
The Pigeon Hole Principle: 7 gorgeous proofs
The ultimate tower of Hanoi algorithm
Переглядів 222 тис.3 роки тому
The ultimate tower of Hanoi algorithm
Explaining the bizarre pattern in making change for a googol dollars (infinite generating functions)
Переглядів 141 тис.3 роки тому
Explaining the bizarre pattern in making change for a googol dollars (infinite generating functions)
The ARCTIC CIRCLE THEOREM or Why do physicists play dominoes?
Переглядів 323 тис.3 роки тому
The ARCTIC CIRCLE THEOREM or Why do physicists play dominoes?
700 years of secrets of the Sum of Sums (paradoxical harmonic series)
Переглядів 776 тис.3 роки тому
700 years of secrets of the Sum of Sums (paradoxical harmonic series)
The hardest "What comes next?" (Euler's pentagonal formula)
Переглядів 744 тис.3 роки тому
The hardest "What comes next?" (Euler's pentagonal formula)

КОМЕНТАРІ

  • @snneakydevil
    @snneakydevil 18 годин тому

    best combo in the era of gaming??? ?

  • @holgerjrgensen2166
    @holgerjrgensen2166 19 годин тому

    Turn a clay-cube, into a ball.

  • @VioletGiraffe
    @VioletGiraffe День тому

    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 День тому

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

  • @user-qe1vz3qw1x
    @user-qe1vz3qw1x День тому

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

  • @LheannMichelleFlorento-xc7ux

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

  • @jjnevis
    @jjnevis День тому

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

  • @joaofrutinho
    @joaofrutinho 2 дні тому

    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?

    • @Chris-5318
      @Chris-5318 День тому

      Try M for Mathologer. What would your question be if he used X instead of M!?

  • @jbruuuu
    @jbruuuu 2 дні тому

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

  • @quantumgaming9180
    @quantumgaming9180 2 дні тому

    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 2 дні тому

    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 ".33...=1/3) minus ".33...") and 1 divided by 3 is not complete.

    • @johnlabonte-ch5ul
      @johnlabonte-ch5ul 2 дні тому

      Any infinitely repeating decimal is incomplete and imprecise.

    • @Chris-5318
      @Chris-5318 День тому

      ​@@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 День тому

      @@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 День тому

      Infinity is incomplete, inconsistent and imprecise.

    • @Chris_5318
      @Chris_5318 День тому

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

  • @mtgatutorials368
    @mtgatutorials368 2 дні тому

    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 2 дні тому

    I think I’m going to teach myself calculus

  • @donwald3436
    @donwald3436 3 дні тому

    Your shirt is too distracting 😂😂😂

  • @3Max
    @3Max 3 дні тому

    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 3 дні тому

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

  • @RichardKandarian
    @RichardKandarian 3 дні тому

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

  • @3Max
    @3Max 4 дні тому

    "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 4 дні тому

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

  • @johannestan8681
    @johannestan8681 4 дні тому

    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 4 дні тому

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

  • @pauselab5569
    @pauselab5569 4 дні тому

    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 5 днів тому

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

  • @ivandrian2
    @ivandrian2 5 днів тому

    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 5 днів тому

    Brilliant

  • @Robloxan899
    @Robloxan899 6 днів тому

    HEW! INF/INF!!!! 😂❤❤😂❤😂❤😂😂❤

  • @Kapomafioso
    @Kapomafioso 6 днів тому

    So question, why didn't you push the point on the circle all the way to its perimeter, so that the star would become sharp, like in the animation? Would that spoil the star somehow?

  • @bmclaughlin01
    @bmclaughlin01 6 днів тому

    It’s easy if you just do the easy stuff. More UA-cam maths, don’t listen to these idiots.

  • @user-ud6ui7zt3r
    @user-ud6ui7zt3r 6 днів тому

    Does this mean that… pi + e …xor… pi TIMES e …has to be rational ?

  • @user-ud6ui7zt3r
    @user-ud6ui7zt3r 6 днів тому

    I think the illustration of an Eagle 🦅 , used by insurance companies, financial businesses, and gun manufacturers, was based upon Hermite’s hair.

  • @pursuitforspeed
    @pursuitforspeed 6 днів тому

    Not a big commenter on videos, but I have to say: What an elegant and brilliant visual representation of Eulers formula.

  • @porzerbuddha
    @porzerbuddha 6 днів тому

    It's interesting, I once took "medicine" with a Native American shaman. I was able to "see" the energy connecting everything, i.e. what one normally sees as empty space between everything. When I tried to describe the structure of the energy, I said it was a combination of bubble wrap and a bee's honey comb, for lack of better description. And I said the magical number is 3. We'll, that vortex in the thumbnail is what I saw, but 3D and barely visible. However, I still think I was just hallucinating and didn't see any objective material. I doubt anyone will read this...😅 but in case you do, Peace and Blessings.

  • @CoollHwhip
    @CoollHwhip 6 днів тому

    9 is the number for consciousness 😊

  • @davidhand9721
    @davidhand9721 7 днів тому

    There's a guy on UA-cam that thinks continued fractions like this explain all of physics, Gavin Wince. The numerology is strong with that one.

  • @davidhand9721
    @davidhand9721 7 днів тому

    I hate numerology so much. Learn another number base, any other number base, and whatever neat little coincidence you've got disappears.

  • @Thankingyou1
    @Thankingyou1 7 днів тому

    Why didn't you use simpler examples? You started out with a great video then your examples are way too complicated.

  • @Thankingyou1
    @Thankingyou1 7 днів тому

    You made a great video but your first example is Way too Complicated.

  • @DesignBySish
    @DesignBySish 7 днів тому

    What do you think about Terrence Howard´s theories?

  • @kafiruddinmulhiddeen2386
    @kafiruddinmulhiddeen2386 7 днів тому

    My son came up with the algebraic proof (second one in this video) by himself after around a day of staring at his piece of paper

  • @derekangel7845
    @derekangel7845 7 днів тому

    Your research makes complete sense. This proves that black holes aren't sucking light out, they're projecting darkness inward by bending around the outside of our space and then getting pulled around and then sucked inside our space from a light vacuum. The "event horizon" is the light in which we see pulling this dark matter into our space. Make sense?

  • @stevefrandsen7897
    @stevefrandsen7897 7 днів тому

    Brilliant and fun video

  • @donwald3436
    @donwald3436 8 днів тому

    Proof by contradiction: 1. assume false statement 2. handwave 3. contradiction QED lol.

  • @donwald3436
    @donwald3436 8 днів тому

    The youtube doors are locked? I want to leave! Let me out!!!!!

  • @noellwilson1273
    @noellwilson1273 8 днів тому

    I’m not sure about the “magic” and the “400 years” but I’m 81, grew up with a slide rule, and still think they are wonderful. As you partly mentioned, logs 1614 by Napier, Log Scale 1620 by Gunter, “sliding scales” in 1622 by Oughtred, and circular sliding scales in 1622(or 1632?) by Oughtred. So, in 20-30 years, we had most of the magic. By the 1960’s we had straight 10” slide rules with 32 scales for, almost, everything (Pickett N3). Unfortunately, we had to wait 400 years for the animated Power Point presentation that makes it jump out at you.

  • @NonTwinBrothers
    @NonTwinBrothers 8 днів тому

    2:24 Just in case UA-cam deletes my comment with a link on it, I found A solution to the Red Cross puzzle in Desmos. I put a link to the graph on my channel about page. Still not sure if it's THE unique solution (I was ready to like, categorize every possible cut you could take haha). Another day perhaps!!

  • @valherustinger7848
    @valherustinger7848 8 днів тому

    that diagram is a graphical representation of analogue sound

  • @pauselab5569
    @pauselab5569 8 днів тому

    3:00 heard it from a lot of people a bit randomly then learned it from a corollary of Gauss's lemma. come on we already had minimal polynomials 5 years ago on this channel... that's a small step away from some field theory

  • @faustobarbuto
    @faustobarbuto 8 днів тому

    I'm amazed that such an educational and well-elaborated video got only 15K thumbs-up in almost eight years. That makes less than 2K thumbs-up per year.

  • @bmaxwell7718
    @bmaxwell7718 9 днів тому

    neither one

  • @yiutungwong315
    @yiutungwong315 9 днів тому

    Put it Harder... In English and German... University 🎓🏫🎓🏫 Universe and Universal ♾️💍 That's Means π = 2 in Riemann Paradox and Sphere Geometry System Incorporated... 1 + 1/2 + 1/4 + 1/8 + ... = 1 + 1 = 2 = π So 1 = 0.999... is Indeed Correct 😄😁💯🔥▶️