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arXiv · 2405.02352

Adventitious angles problem: the lonely fractional derived angle

Yong Kong·Shaowei Zhang
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Abstract

In the "classical" adventitious angle problem, for a given set of three angles $a$, $b$, and $c$ measured in integral degrees in an isosceles triangle, a fourth angle $\theta$ (the derived angle), also measured in integral degrees, is sought. We generalize the problem to find $\theta$ in fractional degrees. We show that the triplet $(a, b, c) = (45^\circ, 45^\circ, 15^\circ)$ is the only combination that leads to $\theta = 7\frac{1}{2}^\circ$ as the fractional derived angle.

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Yong Kong, Shaowei Zhang. 2024-05-02. Adventitious angles problem: the lonely fractional derived angle. https://doi.org/10.4169/amer.math.monthly.123.08.814

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