We say that a triangle T tiles a polygon A, if A can be dissected into finitely many nonoverlapping triangles similar to T. We show that if \(N>42\), then there are at most three nonsimilar triangles T such that the angles of T are rational multiples of \(\pi \) and T tiles the regular N-gon. A tiling into similar triangles is called regular, if the pieces have two angles, \(\alpha \) and \(\beta \), such that at each vertex of the tiling the number of angles \(\alpha \) is the same as that of \(\beta \). Otherwise the tiling is irregular. It is known that for every regular polygon A there are infinitely many triangles that tile A regularly. We show that if \(N>10\), then a triangle T tiles the regular N-gon irregularly only if the angles of T are rational multiples of \(\pi \). Therefore, the number of triangles tiling the regular N-gon irregularly is at most three for every \(N>42\).

我们说一个三角形牛逼瓷砖的多边形一个，如果一个可以被分成有限多个不重叠的三角形相似 牛逼。我们表明，如果\（N> 42 \），则有最多三个为非相似三角形Ť使得所述角度Ť是合理的倍数\（\ PI \）和Ť平铺定期Ñ边形。如果块具有两个角度\（\ alpha \）和 \（\ beta \），则平铺到相似的三角形称为常规三角形，这样在平铺的每个顶点处，角度\（\ alpha \）就是与...相同 \（\ beta \）。否则，拼贴是不规则的。据了解，每正多边形一个有图块无穷多个三角形一个规律。我们证明，如果\（N> 10 \），则仅当T的角度是\（\ pi \）的有理倍数时， 三角形T才会不规则地铺砌规则的N -gon 。因此，对于每个\（N> 42 \），不规则地平铺规则N边的三角形的数量最多为三个。