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An Ellipse Morphs to a Cosine Graph!

L. R. King
The College Mathematics Journal
Vol. 44, No. 2 (March 2013), pp. 117-123
DOI: 10.4169/college.math.j.44.2.117
Stable URL: http://www.jstor.org/stable/10.4169/college.math.j.44.2.117
Page Count: 7
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An Ellipse Morphs to a Cosine Graph!
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Abstract

Summary We produce a continuum of curves all of the same length, beginning with an ellipse and ending with a cosine graph. The curves in the continuum are made by cutting and unrolling circular cones whose section is the ellipse; the initial cone is degenerate (it is the plane of the ellipse); the final cone is a circular cylinder. The curves of the continuum show the ellipse from the perspective of the intrinsic geometry of the various cones.

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