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On some Formulas about Volume and Surface Area

Published online by Cambridge University Press:  22 January 2016

Minoru Kurita
Minoru Kurita*
Affiliation:
Mathematical Institute, Nagoya University
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We prove in this paper some integral formulas about volume and surface area which are the extensions of the classical formulas such as Guldin-Pappus’s theorem about the solid of rotation and the surface of rotation and Holditch’s theorem about the area of the domains bounded by the loci of three points on a segment that moves on the euclidean plane. The formulas we prove are so elementary that they may be found in some literature, but the proofs here given are very simple by the use of moving frames and I assume that they are of some interest.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 6 , October 1953 , pp. 109 - 117
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1953

References

[1] Weyl, H., On the volume of tubes, Amer. J. Math. 61 (1939).CrossRefGoogle Scholar
[2] Cartan, E., Leçons sur la géométrie des espaces de Riemann, Paris, 1946.Google Scholar