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- W2553676507 abstract "If the vertices of a triangle are projected onto a given line, the per- pendiculars from the projections to the corresponding sidelines of the triangle intersect at one point, the orthopole of the line with respect to the triangle. We prove several theorems on orthopoles using the Pappus theorem, a fundamental result of projective geometry. Theorems on orthopoles are often proved with the help of coordinates or com- plex numbers. In this note we prove some theorems on orthopoles by using a well- known result from projective geometry, the Pappus theorem. Notably, we need not even use it in the general case. What we need is a simple affine theorem which is a special case of the Pappus theorem. We denote the intersection of two lines g and g by g ∩ g. Here is the Pappus theorem in the general case. Theorem 1. Given two lines in a plane, letA, B, C be three points on one line and A, B, C three points on the other line. The three points" @default.
- W2553676507 created "2016-11-30" @default.
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- W2553676507 date "2004-01-01" @default.
- W2553676507 modified "2023-09-27" @default.
- W2553676507 title "Orthopoles and the Pappus Theorem" @default.
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