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• 
  @caiofernando8 күн бұрын

  Excellent video.

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  @9WEAVER912 күн бұрын

  A new classic here! I've had this video in my Downloads for some time.

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  @manarsalem168525 күн бұрын

  This was mind-blowing to watch. I'm amazed at how you could convey everything so neatly and clearly.

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  @md.arifulislamroni2946Ай бұрын

  love it;❤

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  @AbjSirАй бұрын

  Thanks.

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  @Intresting-stuffАй бұрын

  Weird how this video was located next to Lemmino's new video

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  @NestPavelАй бұрын

  Came here after Leminno video about Kryptos. Nice video! And the puzzle was fun, althought at first I didn't know what to do with the fact that last row is incomplete. But when you think about it, it becomes more or less obvious.

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  @davethesid8960Ай бұрын

  Really enjoyed this video, gave me a new reason to love maths even more! One tiny note: it should be pronounced "Dirishley".

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  @IptenTАй бұрын

  This is fantastic, thank you!

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  @maynardtrendle8202 ай бұрын

  I think this is a WILDLY helpful video. Awesome job.😎

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  @cupostuff99292 ай бұрын

  7:25 once you dropped down into the origin my brain immediately made the connection between the inverse square law & what was being talked about previously

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  @sasanrahmatian3123 ай бұрын

  At 2:30 you said, “. . . like Pi as the ratio of diameter to circumference”.

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  @coryanders63283 ай бұрын

  This didn't do it for me. I feel as if my understanding has regressed after watching this😢

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  @steveglemaud34593 ай бұрын

  I don't understand shit she said . 😅

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  @locopenguin61613 ай бұрын

  Amazing

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  @aMulliganStew4 ай бұрын

  Hello Dr. Kate. Loved this video. Previously, I was convinced that on the interval [0,1) the number of reals was equivalent the number of whole numbers and that Cantor's diagonal proof was junk. Your video changed my mind about the former. :) Now the proposition that .999-repeating is identical to 1 has re-entered my life. As I currently understand this video, they aren't equal for .999-repeating never intersects 1.0 in the graph. (But, then again, thinking as I type this, It never passes 1-0 either.) For very-part-time, recreational, arm-chair mathematicians like myself, could you maybe, please, discuss .999-repeating and how it is or isn't the same as one? Thanks much if you do. (Pretty much the same if you take a pass.) In either case, thanks for the video.

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  @bartomiejpotaman69734 ай бұрын

  Youre a wonderful teacher. I mean it. You made it very suggestive what the answer is so that I could come up with it myself. Brilliantly done and I bet you - now it is mine forever!

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  @TheWesternPrince4 ай бұрын

  Amazing video! I personally think this explanation is much better than the ones shown on AwesomeMath L4

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  @klevisimeri6075 ай бұрын

  ❤

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  @klevisimeri6075 ай бұрын

  This is the first explanation I have seen that describes the deeper understanding. Plus voice is very calm.

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  @user-ll7mp7qx8d5 ай бұрын

  Nn

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  @cellmaker15 ай бұрын

  Great stuff. However, it would have been useful to show an example where there are no common factors except for 1.

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  @davidhand97215 ай бұрын

  So how big would you need these circles to be in order to crack RSA? You know, hypothetically?

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  @naruhitoabiku94515 ай бұрын

  you are a legend

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  @kikivoorburg5 ай бұрын

  This also sort of explains why the golden ratio φ is like the “most irrational number” - its continued fraction ‘address’ consists of only 1s - so all the rational approximations are similarly bad! Since the coefficients are always natural numbers, 1 is the worst possible! Edit: fixed it’s instead of its.

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  @James22105 ай бұрын

  You can get the circumference of the observable universe to a planck length with only 64 digits if I recall

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  @PaperboySilver5 ай бұрын

  🎯 Key Takeaways for quick navigation: 00:01 📏 *Introduction to real numbers and their representation.* 03:10 🧮 *Decimal expansion, limitations, and notable approximations.* 04:57 🎈 *Visualizing rational numbers, Reuleaux theorem, and their relationship.* 07:25 🌐 *Rational numbers explained through projective geometry.* 09:35 🛣️ *Fairy subdivision, its comparison to decimals, and pi's continued fraction.* 12:57 🥧 *Discovering Pi's true nature via its continued fraction expansion.* Made with HARPA AI

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  @wurnotantmlb5 ай бұрын

  whatttttt this is the most exciting math video that ive seen!!!

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  @buckleysangel70196 ай бұрын

  Beautiful videos!

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  @kindpotato6 ай бұрын

  I haven't even watched the video yet, but I've been a big fan of these kind of fractals since I was young and always wanted to write a program to generate them. I just wrote a program that finds the circles very well for a very specific example. I'm excited to learn more about three circles tangent to each other lol.

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  @henrynwosu62776 ай бұрын

  I wish I could say thank you in person. I am a Mechatronics Engineering Student and we are Studying the Routh-Hourwitz Criterion in Control Systems. I'm trying to understand this so I can understand the proof of the Routh-Hurwitz criterion better. I have to say, you are part of the people that make my degree worthwhile. Thanks so much for what you do. Thanks for not giving up on prooving mathematial facts. Thanks for not giving up on intuition. Thanks for not obscuring mathematical concepts . Thanks for making it accessible. Thank you. Thank you. Thank you !!!!😢😢😢😢😢😢😢.

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  @Aesthetycs6 ай бұрын

  I never thought of continued fractions as binaries.

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  @Halfcast3656 ай бұрын

  when you divide by 6 you get 3 remainder 4? what are you dividing? assuming you are dividing 22 by 6, this is giving us 3.6. could you clarify this part as as you stated it gets tricky but you dont explain the workings of this very clearly

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  @jonahunderhill6 ай бұрын

  Took me a bit to get a proof of multiplication being well defined, but here goes: We have n|a-a' and n|b-b'. We want n|ab-a'b'. Since n|b-b', we get n|a(b-b') since multiplying an arbitrary integer won't change whether it's divisible Since n|a-a', we get n|(a-a')b' for the same reason The sum of 2 things with a common factor will have that same common factor, so n|a(b-b') + (a-a')b' n|ab-ab'+ab'-a'b', distributing the multiplication n|ab-a'b'

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  @ewthmatth6 ай бұрын

  "everyone's favorite, pi" Hmmm, not sure I'm familiar. Is that like half of tau, or something? ;P

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  @carlosraventosprieto20657 ай бұрын

  I LOVED your video named rethinking the real line and now i saw this one and came in to your channel and saw that you are the same person!!! i didnt subscribe 3 months ago but i do now with a smile on my face :)

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  @ghostagent35527 ай бұрын

  Everywhere I go with visual representations for math, I ended up seeing infinitely repeating fractals

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  @carlosraventosprieto20657 ай бұрын

  I LOVE YOUR LETTERS

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  @tunvas7 ай бұрын

  you're a genius

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  @josephhosier77707 ай бұрын

  Is anyone able to help me understand the statement at 13:20? If we take the case of N = 10, which gives quadratic residues mod N of {0,1,4,5,6,9}. The prime divisors of 10 are 2 and 5. The quadratic residues mod 5 are {0,1,4} and those of 2 are {0,1}. x = 5,6 and 9 are all cases where the Fundamental Principle is failing to hold. What am I missing? Is the logic meant to be the other way around?

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  @d.l.74163 ай бұрын

  5,6,9 are 0,1,4 mod 5 and 4,5,6,9 are 0,1,0,1 mod 2 so they are quadratic residues mod 5 and 2

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  @PerryWagle7 ай бұрын

  Thank you very much for the visualizations!

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  @petersmythe64627 ай бұрын

  355/113 really is unbelievably accurate. Specifically, it is 294 times more accurate than it is precise. Compare: 2721/1001 for e, which is only 9 times more accurate than it is precise. 22/7 is 16x more accurate than precise, while 19/7 is only 5x more accurate than precise. π just seems to have several inexplicably good simple rational approximations. Heck, even 3/1 is better at approximating π than e.

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  @petersmythe64627 ай бұрын

  You're basically getting about 2 sig figs for free.

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  @Mark-nm9sm7 ай бұрын

  Thank you so much for making us think

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  @user-vg1br9fx8i7 ай бұрын

  سؤال اتمنى تردي بدري لان بكرا الشرح حقي الحين الارقام513264 منين جبناهن؟!

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  @goldenboy76977 ай бұрын

  You showed a visual proof with the triangles showing that it leaves 3 if the gcd is 3 never breaking part the groups which the amount would be the gcd, but I still dont understand why that works or happens, you just showed that it did, but i don't understand why subtracting it from each side leaves the gcd.

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  @jeffocks7937 ай бұрын

  This has made me very happy. Fabulous

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  @obinnaomego19717 ай бұрын

  I am subscribing

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  @EricSchmeling7 ай бұрын

  I wish this came up in my feed sooner!

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  @nollix8 ай бұрын

  Am I right in saying that there isn't a pattern to the continued fraction basically by definition of an irrational? In other words, if we knew a pattern, we would have a closed form solution for instantly calculating pi to an arbitrary degree of accuracy, which is the same as saying it's rational (contradiction)? Now then I guess what remains is proving that pi is irrational.

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  @silentjazzfool8 ай бұрын

  I like your exposition but the background music makes it impossible for me to concentrate properly on what you're saying so I only got about a third of the way through.