Triangles I: Shapes

@article{Lester1996TrianglesIS,
  title={Triangles I: Shapes},
  author={June A. Lester},
  journal={aequationes mathematicae},
  year={1996},
  volume={52},
  pages={30-54}
}
  • J. Lester
  • Published 1996
  • Mathematics
  • aequationes mathematicae
SummaryThis paper is the first in a series of three examining Euclidean triangle geometry via complex cross ratios. In this paper we show that every triangle can be characterized up to similarity by a single complex number, called its shape. We then use shapes and two basic theorems about shapes to prove theorems about similar triangles. The remaining papers in this series will examine complex triangle coordinates and complex triangle functions. 
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References

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Triangles III: Complex triangle functions
SummaryThis 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. InExpand
Triangles II: Complex triangle coordinates
SummaryThis paper is the second in a series of three examining Euclidean triangle geometry via complex cross ratios. In the first paper of the series, we examined triangle shapes. In this paper, weExpand
Central points and central lines in the plane of a triangle
Triangle geometry ranks among the most enduring topics in all of mathematics. A treasury of triangle lore abounds in Euclid's Elements of 2.3 millenia ago, and still today interesting elementaryExpand
The Penguin Dictionary of Curious and Interesting Geometry
What do the Apollonian gasket, Dandelin spheres, interlocking polyominoes, Poncelet's porism, Fermat points, Fatou dust, the Vodernberg tessellation, the Euler line and the unilluminable room have inExpand
Points of difference: Relative infinity in the Euclidean plane
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