# Solution of Sondow's Problem: A Synthetic Proof of the Tangency Property of the Parbelos

@article{Tsukerman2014SolutionOS, title={Solution of Sondow's Problem: A Synthetic Proof of the Tangency Property of the Parbelos}, author={Emmanuel Tsukerman}, journal={The American Mathematical Monthly}, year={2014}, volume={121}, pages={438 - 443} }

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.

## 3 Citations

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A parabolic analog of the arbelos is introduced, using theorems of Archimedes and Lambert to demonstrate seven properties of the parbelos, drawing analogies to similar properties ofThe arbelo, some of which may be new.

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A variety of new proofs of Campbell’s hypergeometric formula for the parbelos constant S are offered, including a creative proof that makes use of a Fourier–Legendre expansion.

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