Triangles. I: Shapes
type: Item
instance of: scholarly article
title: Triangles. I: Shapes
zbMATH Open document ID: 0860.51009
DOI: 10.1007/BF01818325
published in: Aequationes Mathematicae
publication date: 1997-02-26T00:00:00Z
full work available at URL: https://eudml.org/doc/137653
review text: This is the first of a series of three papers that examine Euclidean triangle geometry via complex cross-ratios [as developed, for example, by \textit{I. M. Yaglom} in his book `Complex numbers in geometry', Academic Press, New York (1966; Zbl 0147.20201)]. In this first paper, the author examines analytic methods for proving similarity theorems. She observes that, by using cross-ratios, any Euclidean triangle may be classified up to similarity by a single complex number, which she calls the shape of the triangle. In particular, she discusses the shapes of Miquel triangles. Finally, she examines two general shape theorems, the second of which has the theorems of Napoleon and Morley as special cases.
reviewed by: E. J. F. Primrose
Mathematics Subject Classification ID: 51M05
Mathematics Subject Classification ID: 51N20
zbMATH DE Number: 935126
zbMATH Keywords: Euclidean triangle geometry
zbMATH Keywords: complex cross-ratios
zbMATH Keywords: similarity
zbMATH Keywords: shape
Wikidata QID: Q64356242
author: June A. Lester
MaRDI profile type: Publication
cites work: Q5848645
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cites work: Q4293427
cites work: Triangles. II: Complex triangle coordinates
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cites work: Q5687946
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description: scientific article; zbMATH DE number 935126