The Sphere in 3-Space

Gerhard P. Hochschild
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Gerhard P. Hochschild: University of California, Department of Mathematics

Chapter Chapter IX in Perspectives of Elementary Mathematics, 1983, pp 107-117 from Springer

Abstract: Abstract Let V be a Euclidean space, W an m-dimensional sub R-space of V, p a point of V. Then the subset p + W is called an m-dimensional affine subspace of V. Suppose that f is an injective linear map from R m to W, and let B be a block in R m . Then f(B) is a parallelepiped in W, and therefore has m-volume. As is evidently appropriate, we define the m-volume of the subset p + f(B) of the affine space p + W to be the m-volume of f(B). We refer to p + f(B) as an affine m-patch in V.

Keywords: Pairwise Disjoint; Great Circle; Euler Characteristic; Numerical Measure; Unit Quaternion (search for similar items in EconPapers)
Date: 1983
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DOI: 10.1007/978-1-4612-5567-3_9

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