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Re: Help on tetrahedrons
Posted:
Jun 16, 1996 6:03 PM


In article <4poknv$9jo@rzsun02.rrz.unihamburg.de>, fc3a501@GEOMAT.math.unihamburg.de (Hauke Reddmann) writes: > Maciej Kosinski (atomko1@ato.abb.se) 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 coords (1,1,1) (1,1,1) (1,1,1) (1,1,1) are the vertices of a tetrahedron centered at the origin.
Use the dot product to obtain cos(t) = 1/3
Ian H



