Abstract
It is impossible to trisect an arbitrary angle (divide the angle into three equal parts) using only a straightedge and compass. Trisection requires the construction of cube roots, but a straightedge and compass can only construct lengths that are expressions built from integers, the four arithmetic operators and square roots. This was proved by Pierre Wantzel in 1837. Nevertheless, innumerable amateurs continue to attempt to trisect an angle. Their constructions are approximations though they are convinced that the constructions are correct. Section 2.1 presents two such constructions, develops formulas for the angles and shows the errors in the approximations.
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Ben-Ari, M. (2022). Trisection of an Angle. In: Mathematical Surprises. Springer, Cham. https://doi.org/10.1007/978-3-031-13566-8_2
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DOI: https://doi.org/10.1007/978-3-031-13566-8_2
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-031-13566-8
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