$\mathbb{Z}\times\mathbb{Z}$中的格点所形成的 有理度角 必为 45° 的整数倍

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jstor.org/stable/2691462 写道：

Corollary 3. On the "square geoboard" (the lattice Z x Z in $\mathbb R^2$), the only angles of rational measure (in degrees) that can be formed by three lattice points are integer multiples of 45°. (This was conjectured in 1921 [26] and first proved in 1945 [20].)

$\mathbb{Z}\times\mathbb{Z}$中的格点所形成的 有理度角 必为 45° 的整数倍。
如何证明？

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顶一下