Abstract In 1934, B. Berggren first discovered the surprising result that every Pythagorean triangle is the pre-product of the triangle (3, 4, 5) given as a column vector by a product of three matrices, and that every triangle is obtained in this manner exactly once and in primitive form. In this article, we show a similar result for integer triangles with an angle of 60 and 120 degrees (also known as Eisensteinian triangles). We show that any such triangle is obtained by pre-multiplication of (7, 8, 5) or (13, 15, 7) by a product arising from a set of five matrices.

中文翻译：

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爱森斯坦三角形的森林

摘要 1934 年，B. Berggren 首次发现了一个令人惊讶的结果，即每个勾股三角形都是由三个矩阵的乘积作为列向量给出的三角形 (3, 4, 5) 的前积，并且每个三角形都由这种方式恰好一次并且以原始形式。在本文中，我们展示了角度为 60 度和 120 度的整数三角形（也称为爱森斯坦三角形）的类似结果。我们表明，任何这样的三角形都是通过 (7, 8, 5) 或 (13, 15, 7) 与一组五个矩阵产生的乘积的预乘获得的。