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A Note on the Angles in an n-Dimensional Simplex

Published online by Cambridge University Press:  18 May 2009

A. P. Guinand
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Three different sets of equations connecting the sums of angles in an n-dimensional simplex have been given by Sommerville [7], Höhn [5], and Peschl [6]. The equivalence of the first two sets of equations has been proved by Sprott [7].

In the present note it is shown that results are simplified if we consider averages instead of sums, and that the averages form a sequence which is self-reciprocal with respect to the transformation

The equivalence of the sets of equations is then easily proved by symbolic methods.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 2 , July 1959 , pp. 58 - 61
Copyright
Copyright © Glasgow Mathematical Journal Trust 1959

References

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