Area, Volume, Measure

Andrew McFarland, Joanna McFarland and James T. Smith
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James T. Smith: San Francisco State University, Department of Mathematics

Chapter 4 in Alfred Tarski, 2014, pp 45-76 from Springer

Abstract: Abstract The synthetic approach to the theory of area and volume initiated by Euclid is described in the first section of this chapter. The area a of a polygonal region P is computed by decomposing P into a finite number of polygonal components with disjoint interiors, which can be reassembled to form a rectangle R with unit base: a is then the altitude of R. The volume of a polyhedral region can be reckoned in a similar way, but for that it is necessary to use some form of Eudoxus’s method of exhaustion.

Keywords: Disjoint Subset; Measure Problem; Polygonal Region; Disjoint Interior; Bernstein Theorem (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-1474-6_4

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DOI: 10.1007/978-1-4939-1474-6_4

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