Question

3 dimensional geometry puzzle.

Answer 1

Imagine a sphere and its centre. Have 4 lines go out from the centre to touch the sphere and a red dot marks where it touches the sphere. The red dots are as far apart from each other as possible. Now, visualise the flat plane that line 1 and 2 inhabit. Note the angle between the lines on this plane. Repeat for the 2-3, 3-4 and 4-1 plane. What is the sum of all the angles measured?

This is easy to calculate, as the 4 lines will just form a tetrahedron. But is there a formula linking the number of lines, n, with the sum of the angles?

Answer 2

This question in fact arises from a simplified view of bond angles of a molecule.

Answer 3

can you draw your picture?

Answer 4

n=1