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Solution of Sondow’s Problem: A Synthetic Proof of the Tangency Property of the Parbelos
The American Mathematical Monthly
Vol. 121, No. 5 (May 2014), pp. 438-443
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.05.438
Page Count: 6
You can always find the topics here!Topics: Parabolas, Tangents, Rectangles, Mathematical cusps, Geometric angles, Mathematical theorems, Tangent lines, Vertices, Mathematical induction, Billiards
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Abstract In a recent paper titled The parbelos, a parabolic analog of the arbelos, Sondow asks for a synthetic proof to the tangency property of the parbelos. In this paper, we resolve this question by introducing a converse to Lambert’s Theorem on the parabola. In the process, we prove some new properties of the parbelos.
Copyright the Mathematical Association of America 2014