论文标题
庞贝定理和三角形的模量空间
Pompeiu's theorem and the moduli space of triangles
论文作者
论文摘要
我们介绍了庞贝定理的一种相反。修复一个等边三角形$ \ triangle a_0b_0c_0 $，然后对于任何三角形$ \ triangle abc $，包皮环circle $ quircircle $γ_0$ \ triangle a_0b_0c_0 $ a_0b_0c_0 $ a_0b_0c_0 $ a_0b_0c_0 $的唯一点$ p $与Edge length length length length length length Lengths $ pa_0 $ pa_0 $ $ $ pc_ $ pc $ pc $ pc $ \ pc $ pc $ \ pc $ \ pc $ \。因此，可以将$γ_0$内部的开放光盘视为三角形相似性类别的模量空间。我们表明，它基本上等同于基于三角形的形状函数的另一个模量空间，该函数已用于先前的研究。
We introduce a kind of converse of Pompeiu's theorem. Fix an equilateral triangle $\triangle A_0B_0C_0$, then for any triangle $\triangle ABC$ there is a unique point $P$ inside the circumcircle $Γ_0$ of $\triangle A_0B_0C_0$ such that a triangle with edge lengths $PA_0, PB_0$, and $PC_0$ is similar to $\triangle ABC$. It follows that an open disc inside $Γ_0$ can be considered as a moduli space of similarity classes of triangles. We show that it is essentially equivalent to another moduli space based on a shape function of triangles which has been used in preceding studies.
