A proof without words that

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + … = 1

🤓 pic.twitter.com/VaUBqn3twh

— Fermat's Library (@fermatslibrary) April 22, 2021

Imagine a string streaming in a current. In something like a whirlpool, the string would form a loop. A vortex ring might make a knotted loop.

Wild question: Is there a single current that can tie ~every~ knot?

🧵/ pic.twitter.com/FtXBBthRpt

— chessapig (@chessapigbay) April 15, 2021

Everyone knows that all circles are similar. But did you know that all parabolas are similar?

The ratio of the red parabolic arc length and the blue focal parameter is
√2 + log(1+√2) = 2.29558…
for any parabola. This is the universal parabolic constant, the “π of parabolas”. pic.twitter.com/JntitYWd7q

— Tamás Görbe (@TamasGorbe) April 3, 2020

Pick uniformly distributed random points in a 6×6 square. The average distance from the centre is
√2 + log(1+√2) = 2.29558…

It's the universal parabolic constant! How crazy is that‽ Where is the parabola in this problem about random points in a square??? pic.twitter.com/AOnYPFNubR

— Tamás Görbe (@TamasGorbe) April 4, 2020

A final surprise! We can connect e, π, and the universal parabolic constant.

Plot the function y=exp(-x) over the positive x-axis and rotate the graph about the x-axis. The surface you get has area π × the parabolic constant. pic.twitter.com/jL13wWpRBv

— Tamás Görbe (@TamasGorbe) April 4, 2020