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In the transformations considered so far, we have worked in either the real plane, represented as the set of ordered pairs of real numbers, or the extension of the real plane to the real projective plane, where one point at infinity is added to every finite line, with the collection of those points at infinity forming, itself, the line at infinity. Now we will study two other transformations in which there is just one point at infinity, a point shared by all lines.

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Geometric Inversion

  • 章节

  • 发表日期：

    2025年

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  • Christopher Baltus

摘要

In the transformations considered so far, we have worked in either the real plane, represented as the set of ordered pairs of real numbers, or the extension of the real plane to the real projective plane, where one point at infinity is added to every finite line, with the collection of those points at infinity forming, itself, the line at infinity. Now we will study two other transformations in which there is just one point at infinity, a point shared by all lines.