Everyone knows that all circles are similar. But did you know that all parabolas are similar?
— Tamás Görbe (@TamasGorbe) April 3, 2020
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
Pick uniformly distributed random points in a 6×6 square. The average distance from the centre is
— Tamás Görbe (@TamasGorbe) April 4, 2020
√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
A final surprise! We can connect e, π, and the universal parabolic constant.
— Tamás Görbe (@TamasGorbe) April 4, 2020
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