Doubling the Cube and Constructability in Higher Dimensions

Q4 Mathematics
Julius B. Barbanel
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引用次数: 0

Abstract

Summary It is known that the three classical geometric construction problems introduced by the ancient Greeks: trisecting an angle, squaring a circle, and doubling a cube, cannot be solved using the Euclidean tools. However, ancient Greek mathematicians solved these three problems using other means. We present solutions to the doubling-the-cube problem using ideas that go beyond the Euclidean tools, and we consider generalizations to higher dimensions.
多维立方体的加倍与可构造性
众所周知,古希腊人提出的三个经典几何构造问题:角的三分、圆的平方和立方体的加倍,是无法用欧几里得工具解决的。然而,古希腊数学家用其他方法解决了这三个问题。我们使用超越欧几里得工具的思想提出了立方体加倍问题的解决方案,我们考虑将其推广到更高的维度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mathematics Magazine
Mathematics Magazine Mathematics-Mathematics (all)
CiteScore
0.20
自引率
0.00%
发文量
68
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