Curves and Surfaces

A. Gardiner
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A. Gardiner: University of Birmingham, Department of Mathematics

Chapter Chapter III.5 in Infinite Processes, 1982, pp 232-243 from Springer

Abstract: Abstract Like rulers themselves, length and distance are essentially “straight,” 1-dimensional concepts; similarly area is an essentially “flat,” 2-dimensional concept. Yet both concepts are used in other contexts: we do not restrict our attention solely to lengths of straight line segments, but are also interested in “lengths of curves”, such as the circle, or the cycloidal arch (Exercise 1); and we refer to “the area” not just of flat 2-dimensional shapes, but also of curved surfaces such as the cone, cylinder,1 and sphere. We shall end Part III by inquiring a little more closely how these extended notions of length and area can be justified, though we shall not come to any final conclusion.

Date: 1982
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DOI: 10.1007/978-1-4612-5654-0_20

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