Maximizing the Area of a Sector With Fixed Perimeter
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Date
2010
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Publisher
Ohio Council of Teachers of Mathematics
Abstract
Historically, many maxima and minima were found long before Newton and Leibniz developed calculus. Ivan
Niven's (1981) classic Maxima and Minima Without Calculus provides a systematic and thorough account
of solving extreme-value problems using elementary algebra, geometry, and trigonometry. Niven devotes a
chapter to isoperimetric problems: problems that ask "for the region of largest area in a given class of regions ... of a specified perimeter" (p. 77). We use technology as a tool to solve the isoperimetric problem for the
sector of a circle—an investigation inspired by a project in Farrell and Boyd (2007).
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Citation
Ohio Journal of School Mathematics, no. 62 (2010), 17-22.