What are the odds that 3 'random' points on a sphere will form an acute triangle?

The video tutorial explores the problem of selecting points on a sphere to form an acute triangle. It explains how symmetry can simplify the problem, reducing it to a 2D analysis. The tutorial derives a formula to maximize the probability of forming an acute triangle and calculates the optimal angle between the first two points. The solution involves understanding geometric properties and applying calculus to find the optimal configuration, resulting in a probability linked to the golden ratio.

How does the concept of symmetry apply to the selection of points on a sphere?

Describe the formula for calculating the surface area between two parallel planes slicing a sphere.

What is the optimal angle for separating the two points to maximize the winning surface area?