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Area, Volume, Measure

In: Alfred Tarski

Author

Listed:
  • Andrew McFarland
  • Joanna McFarland
  • James T. Smith

    (San Francisco State University, Department of Mathematics)

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.

Suggested Citation

  • Andrew McFarland & Joanna McFarland & James T. Smith, 2014. "Area, Volume, Measure," Springer Books, in: Andrew McFarland & Joanna McFarland & James T. Smith (ed.), Alfred Tarski, edition 127, chapter 4, pages 45-76, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-1474-6_4
    DOI: 10.1007/978-1-4939-1474-6_4
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