An Odd Property of the Sierpiński Triangle - Numberphile

Discussing the Sierpiński Triangle, Fermat Primes, and Constructible Polygons.

Constructible Polygons...

NUMBERPHILE

Videos by Brady Haran

[jayluck]

I love the way she can draw triangles with so much equilaterality.

[rogerkearns]

Amazing. The moment you said, convert to binary, I saw it - but the effect not continuing forever, I didn't see.

[element_]

My heart broke at 9:48 "until row 33".

[hepiik.]

It might be weird, but, as a Pole, seeing a properly written polish name made me smile

[MonsieurBiga]

Ayliean : you can timelapse this
Brady : don't tell me what to do

[betoneiracromadarebaixada]

the Sierpinski triangle really just randomly jumpscares people when it feels like it

[McLir]

Take Pascal's Triangle and dot out all the odd numbers — that also gives a Sierpinski triangle. Seashells can also produce Sierpinski-like patterns.

[kirillsukhomlin]

And if you just take Pascal triangle mod 2, there would be proper infinitely growing Sierpinski triangle.

[JohnRunyon]

I love the shell tattoo while talking about pretty math drawings 😂

[thatonedynamitecuber]

That is the straightest triangle i have ever seen.

To clarify I mean by hand not by any other means

[NatiNugasu]

Ayliean: timelapse this Brady
Brady: 👍
*awkward silence*

[TheArizus]

Fun side note, one of the problems on the 2023 British Algorithmic Olympiad was related to finding rows of the Sierpinski triangle when written in binary (similar to this)

[morganconnelly]

Ah Ayliean coming back again with the amazing content! I love seeing her come back to the channel with her incredible mathematical story telling

[HoSza]

Ok, let's just name it The Parker Triangle.😂

[Bronzescorpion]

The 15 in binary mistake was somewhat funny considering Ayliean pointed out how close it was to 16. Even without giving it much thought, one could easily conclude that it must then be a row of ones, as all the numbers that are 2^n-1 must follow this pattern, before the next number ie. the number that is a power of two rolls over and becomes a number with a 1 followed by a string of zeroes (equal to n).

[kappasphere]

I think an interesting way to generate an image of a sierpinski triangle is to take every pixel coordinate (x, y), and color the pixel if x & y == 0, where "&" is the bitwise and operator.

[josephpk]

Neat to see this geometry again. I just designed a 3d model based on Sierpiński's Triangle, which is a 3D rendered pyramid of the 2D fractal, but I took it a step further and actually modelled the negative space, then printed out these interesting cubes composed of negative and positive 3-sided pyramids - beautiful things, especially when printed with clear materials.

[happyvirus]

5:08 and the length from that point to the edge of the circle is the *golden ratio*

[oliverfalco]

4:25 Looking at someone making a pentagon with compass and ruler is always so exciting :3

[jaymanier]

"Timelapse this."

"...No."

😄