This article explains why a paper by Heinz G. Helfenstein entitled Ovals with equichordal points, J. London Math. Soc. 31 (1956), 54-57, is incorrect. We point out a computational error which renders his conclusions invalid. More importantly, we explain that the method presented there cannot be used to solve the equichordal point problem. Today, there is a solution to the problem: Marek R. Rychlik, A complete solution to the equichordal point problem of Fujiwara, Blaschke, Rothe and Weizenböck, Inventiones Mathematicae 129 (1997), 141-212. However, some mathematicians still point to Helfenstein's paper as a plausible path to a simpler solution. We show that Helfenstein's method cannot be salvaged. The fact that Helfenstein's argument is not correct was known to Wirsing, but he did not explicitly point out the error. This article points out the error and the reasons for the failure of Helfenstein's approach in an accessible, and hopefully enjoyable way.
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机译：本文解释了为什么亨氏·赫尔芬斯坦（Heinz G. Helfenstein）发表题为带等弦点的椭圆的论文J. London Math。 Soc。 31（1956），第54-57页不正确。我们指出了一个计算错误，使他的结论无效。更重要的是，我们解释说那里提出的方法不能用来解决等弦点问题。如今，有一个解决方案：Marek R. Rychlik，《藤原，Blaschke，Rothe和Weizenböck的等弦点问题的完整解决方案，Inventions Mathematicae 129（1997），141-212。但是，一些数学家仍然指出Helfenstein的论文是通向更简单解决方案的合理途径。我们表明，Helfenstein的方法无法挽救。维尔辛知道海尔芬斯坦的说法不正确，但他没有明确指出这一错误。本文以可访问且希望令人愉快的方式指出了Helfenstein方法的错误和失败的原因。
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