In article <email@example.com>, fc3a501@GEOMAT.math.uni-hamburg.de (Hauke Reddmann) writes: > Maciej Kosinski (firstname.lastname@example.org) wrote: > : How to prove that the angule of the regular tetrahedron is 109 > : degrees (or was it 109,5 degrees) in NH3 molecule? > > Old trick: Use CH4 instead. All coordinates must sum to zero > by symmetry, so if one H is at (1,0,0), the rest is at (-1/3,?,??). > You make take ? as 0. Apply vector cosinus. cos(angle)=-1/3.Done.
A better idea is to note that the points with co-ords (1,1,1) (1,-1,-1) (-1,1,-1) (-1,-1,1) are the vertices of a tetrahedron centered at the origin.