Summary
This paper is the third in a series of three examining Euclidean triangle geometry via complex cross ratios. In the first two papers, we looked at triangle shapes and triangle coordinates. In this paper, we look at the triangle coordinates of the special points of a triangle, and show that they are functions of its shape. We then show how these functions can be used to prove theorems about triangles, and to gain some insight into what makes a special point of a triangle a centre.
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References
Eddy, R. H. andFritsch, R.,The conics of Ludwig Kiepert: a comprehensive lesson in the geometry of the triangle. Math. Mag.67 (1994), 188–205.
Gallatly, W.,The modern geometry of the triangle, 2nd edition. Hodgson, London, 1913.
Gale, D.,From Euclid to Descartes to Mathematica to oblivion? Mathematical entertainments (column) in Math. Intelligencer40 (1992), no. 2.
Kimberling, C.,Solution to problem 1685, Crux Mathematicorum. November 1992, 276–278.
Kimberling, C.,Functional equations associated with triangle geometry. Aequationes Math.45 (1993), 127–152.
Kimberling, C.,Central points and central lines in the plane of a triangle. Math. Mag.67 (1994), 163–187.
Lester, J. A.,Triangles I: Shapes. Aequationes Math.52 (1996), 30–54.
Lester, J. A.,Triangles II: Complex triangle coordinates. Aequationes Math.52 (1996), 215–245.
Cabi-géomètre v. 2.1. Brooks Cole, Pacific Grove, CA, 1992.
Geometer's sketchpad v. 2.1. Key Curriculum Press, Berkeley, CA, 1994.
Theorist v. 1.01. Prescience, San Francisco, CA, 1989.