Area-Preserving Transformations: Cavalieri in 2D

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  • 1 Teachers College, Columbia University, New York City
  • 2 Rutgers University, New Brunswick, New Jersey
  • 3 Temple University, Philadelphia, Pennsylvania
  • 4 Rutgers University

A 2D version of Cavalieri's Principle is productive for the teaching of area. In this manuscript, we consider an area-preserving transformation, “segment-skewing,” which provides alternative justification methods for area formulas, conceptual insights into statements about area, and foreshadows transitions about area in calculus via the Riemann integral.

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Footnotes

A two-dimensional segment-skewing version of Cavalieri's principle presents alternative justification methods for formulas as well as conceptual insights into statements about area that foreshadow transitions in calculus via the Riemann integral.

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Mathematics Teacher: Learning and Teaching PK-12
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