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A nomogram for the law of direction-cosines

Published online by Cambridge University Press:  14 March 2018

S. I. Tomkeieff
S. I. Tomkeieff*
Affiliation:
King's College, University of Durham, Newcastle-upon-Tyne
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Extract

If α, β, and γ are the three angles between a line passing through the origin and the three rectangular co-ordinate axes, then the equation connecting them is as follows:

cos2α+cos2β+cos2γ = 1.

This is the law of direction-cosines of a line.

Substituting (cos 2α+1)/2 for cos2α, &c., we get:

cos 2α+cos 2β+cos 2γ = −1.

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 26 , Issue 179 , December 1942 , pp. 272 - 273
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1942

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