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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.02352 |
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| _version_ | 1866909189041815552 |
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| author | Kong, Yong Zhang, Shaowei |
| author_facet | Kong, Yong Zhang, Shaowei |
| contents | 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 $θ$ (the derived angle), also measured in integral degrees, is sought. We generalize the problem to find $θ$ in fractional degrees. We show that the triplet $(a, b, c) = (45^\circ, 45^\circ, 15^\circ)$ is the only combination that leads to $θ= 7\frac{1}{2}^\circ$ as the fractional derived angle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02352 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adventitious angles problem: the lonely fractional derived angle Kong, Yong Zhang, Shaowei Classical Analysis and ODEs 51M04 (Primary) 12F05, 33B10 (Secondary) 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 $θ$ (the derived angle), also measured in integral degrees, is sought. We generalize the problem to find $θ$ in fractional degrees. We show that the triplet $(a, b, c) = (45^\circ, 45^\circ, 15^\circ)$ is the only combination that leads to $θ= 7\frac{1}{2}^\circ$ as the fractional derived angle. |
| title | Adventitious angles problem: the lonely fractional derived angle |
| topic | Classical Analysis and ODEs 51M04 (Primary) 12F05, 33B10 (Secondary) |
| url | https://arxiv.org/abs/2405.02352 |