AI 中文总结
研究特殊平面三角形鼓被敲击的位置，通过证明得出能听到等边和等腰直角三角形被敲击位置，且30 - 60 - 90三角形有两个听觉不可区分点，为首例拓扑连通此类情况。
AI 中文摘要
我们研究对于一些特殊平面三角形，是否能听到鼓在什么点（对称意义下）被敲击。证明了能听到等边三角形和等腰直角三角形被敲击的位置，还证明了30 - 60 - 90三角形有两个听觉上无法区分的点，这是首个此类拓扑连通的已知例子。
英文摘要
We investigate whether or not one can hear at what point (up to symmetry) a drum is struck for some special planar triangles. We prove that one can hear where the equilateral and isosceles right triangles are struck. We also prove that the 30-60-90 triangle, surprisingly, has two audibly indistinguishable points. This is the first known topologically connected such example.
Comments29 pages, 8 figures
