# What is the 3d average of a right angle? [closed]

Imagine to have a right angle in 3d space, like a large capital "L" floating in space.

Averaged from all observation directions, what is the average projected/visible angle of the "L" shape?

(Of course, the legs of the "L" are supposed to be infinitely thin and long.)

Usual disclaimer: this is not homework; it is a question that arose in discussions. Is the average different from a right angle? What is the simplest way to answer the question?

Edit: as MvG mentioned, the average of the absolute angle is meant.

• I assume you mean the absolute value of the angle, because of you were to consider oriented angles, then for reasons of symmetry the positive and the negative contributions would cancel out and leave you with a zero average. Have you tried a Monte Carlo simulation to get a rough idea of what the answer should approximately be?
– MvG
Apr 23 at 8:25
• Yes, I mean the absolute angle. No, I have not yet tried a simulation. A good idea! Apr 23 at 8:51