# 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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