Відео

i watched your video a few months ago and ive been thinking about it constantly, its changed the way i view number! super thanks!

Love you

I am interested in understanding how things work rather than memorization, and in less than a minute of the video, I knew it was special. Content such is this is absolutely vital. Thanks.

Beautiful

This is brilliant. Please continue to make more such videos. This is how science and math must be seen.

At first, I didn't quite grasp why would the GCD remain same after we delete the smaller number from larger one (B-A). But it made sense this way: Hint: We are deleting pile A from pile B and then ask what's the new GCD of leftover pile B and the pile A? Well, just remember, the deletion is also made of new GCD as we just deleted pile A- hence the whole pile B and pile A have a new GCD ;) contradiction ! Explanation: GCD is basically the largest chunk of stones that will divide both piles in some number of parts, say- xa and xb. So, pile A has xa number of GCDs and pile B has xb number of GCDs (largest chunks common for both). => A = g . xa and B = g . xb (Imagine them as bigger balls that make up the pile) Now, we remove just one copy of pile A from B. This means: => B - A = g . xb - g . xa For a moment, let's assume, the common chunk size of A and B-A, could maybe get bigger after deletion- to say g' (read: g dash) => B - A = g' . x' and A = g' . xa' This means, the leftover of pile B is made of g' size chunks with count as x' and pile A is made of g' size chunks with count as xa'. But, here's the catch: the deleted pile A from pile B must also be made of g' size chunks with count as xa'. That means: => deleted pile A + left over pile B = the original pile B => g' . xa' + g' . x' = pile B => g' (xa' + x') = pile B So, the pile B is made of g' size chunks AND pile A is also made of g' size chunks! A common divisor for A and B! What's the largest common divisor for A and B? => The GCD(A, B) = g Hence, g' = g, the original GCD of A and B!

WOW. You explain stuff in such an intuitive manner

This should be first hit for Euclidean algorithm

our explanations are similar except I cut the box Into Identical sections

Excellent video.

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

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

love it;❤

Thanks.

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

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.

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

This is fantastic, thank you!

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

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

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

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

I don't understand shit she said . 😅

Amazing

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.

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!

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

❤

Nn

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

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

you are a legend

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.

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

🎯 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

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

Beautiful videos!

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.

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 !!!!😢😢😢😢😢😢😢.

I never thought of continued fractions as binaries.

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

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'

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

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 :)

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

I LOVE YOUR LETTERS

you're a genius

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?

Thank you very much for the visualizations!

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.