Say the diameter is a segment from A=(a,b) to B=(c,d). A point C=(x,y) on the circle forms a *right* triangle with those two points (Thales!), so the vectors AC and BC are orthogonal, so their slopes are negative reciprocals. That is,
A remarkable result on the ArXiv tonight, due to Kedlaya, Kolpakov, Poonen, and Rubinstein, at https://t.co/YNcWqgZj3M. One of the highlights is that they fully classify tetrahedra (= triangular pyramids) with rational dihedral angles. Here's what they prove… (1/n)
If you cut a mobius strip into thirds, you get two mobius strips! And they're intertwined! And one is bigger than the other! (compare with cutting a cylinder into thirds, which would give you 3 separate equally sizedcylinders) pic.twitter.com/m85h5OKJtZ
Involutes are great! They allow for a nice geometric interpretation of the power series cos(x) = 1 – x²/2! + x⁴/4! – … and sin(x) = x – x³/3! + x⁵/5! – …https://t.co/AGT6VxaD5b