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A Vector Approach to Ptolemy's Theorem

by Erwin Just (Bronx Communty College of the City College of New York) and Norman Schaumberger (Bronx Communty College of the City College of New York)

This article originally appeared in:
Mathematics Magazine
December, 2004

Subject classification(s): Several Variable Calculus | Calculus | Polygons | Plane Geometry | Geometry and Topology
Applicable Course(s): 4.9 Geometry | 3.3 Mainstream Calculus III, IV

Ptolemy's Theorem states that the product of the diagonals of a cyclic quadrilateral (a quadrilateral that can be inscribed in a circle) is equal to the sum of the products of the opposite sides. The authors give a new proof making use of vectors.

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Capsule Course Topic(s):
Multivariable Calculus | History of Multivariable Calculus
Multivariable Calculus | Vector Operations
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