A Ceva point of a rational-sided triangle is any internal or external point such that the lengths of the three cevians through this point are rational. Buchholz [Buc89] studied Ceva points and showed a method to construct new Ceva points from a known one. We prove that almost-equilateral and equilateral rational triangles have infinitely many Ceva points by establishing a correspondence to points in certain elliptic surfaces of positive rank.

中文翻译：

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在（几乎）等边三角形的Ceva点上

有理边三角形的Ceva点是任何内部或外部点，因此三个cevian到该点的长度是有理的。Buchholz [Buc89]研究了Ceva点，并展示了一种从已知点构建新Ceva点的方法。我们通过建立与某些正阶椭圆曲面中点的对应关系，证明几乎等边和等边的有理三角形具有无限多个Ceva点。