论文标题
将正方形解剖为一致的多边形
Dissecting a square into congruent polygons
论文作者
论文摘要
我们研究了正方形的解剖分解为一致的凸多边形。 yuan \ emph {et al。} [将正方形分解为五个一致的部分，离散数学。 \ textbf {339}（2016）288-298]问，瓷砖的数量是否为质量数$ \ geq 3 $，确实必须是矩形。 我们猜想，即使瓷砖的数量为奇数$ \ geq 3 $，同一结论仍然存在。 我们的猜想已在早期作品中得到证实。我们证明，如果任何一个瓷砖是凸$ q $ -gon，则具有$ q \ geq 6 $，或者是右角梯形。
We study the dissection of a square into congruent convex polygons. Yuan \emph{et al.} [Dissecting the square into five congruent parts, Discrete Math. \textbf{339} (2016) 288-298] asked whether, if the number of tiles is a prime number $\geq 3$, it is true that the tile must be a rectangle. We conjecture that the same conclusion still holds even if the number of tiles is an odd number $\geq 3$. Our conjecture has been confirmed for triangles in earlier works. We prove that the conjecture holds if either the tile is a convex $q$-gon with $q\geq 6$ or it is a right-angle trapezoid.
