好事成三:三角三元组的三元树

Q4 Mathematics
Jeremiah Bartz
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引用次数: 0

摘要

俗话说好事三分来。1934年,B.Berggren在发掘三个矩阵时可能达成了一致,这三个矩阵从最初的三元组生成了所有原始勾股三元组的三元树。我们证明了用三角三元组替换原始勾股三元组时也存在类似的结构。两个三元树的构造是相互交织的,涉及Berggren的三个矩阵和第三个三元树法。也许好事真的是三分之一!
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Good Things Come in Threes: A Ternary Tree for Triangular Triples
Summary A common saying is that good things come in threes. In 1934, B. Berggren may have agreed when unearthing three matrices which generate a ternary tree of all primitive Pythagorean triples from the initial triple . We show that a similar structure exists when replacing primitive Pythagorean triples with triangular triples. The construction of both ternary trees are intertwined, involving Berggren’s three matrices and a third ternary tree. Perhaps good things really do come in threes!
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来源期刊
Mathematics Magazine
Mathematics Magazine Mathematics-Mathematics (all)
CiteScore
0.20
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0.00%
发文量
68
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