Maximizing the Area of a Sector With Fixed Perimeter
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Publisher:Ohio Council of Teachers of Mathematics
Citation:Ohio Journal of School Mathematics, no. 62 (2010), 17-22.
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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