Counting the number of isosceles triangles in rectangular regular grids

Final version in Forum Geometricorum, vol. 17, pp. 31-39, 2017 In general graph theory, the only relationship between vertices are expressed via the edges. When the vertices are embedded in an Euclidean space, the geometric relationships between vertices and edges can be interesting objects of study...

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Bibliographic Details
Main Author Wu, Chai Wah
Format Journal Article
LanguageEnglish
Published 30.04.2016
Subjects
Mathematics - Combinatorics
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Summary:Final version in Forum Geometricorum, vol. 17, pp. 31-39, 2017 In general graph theory, the only relationship between vertices are expressed via the edges. When the vertices are embedded in an Euclidean space, the geometric relationships between vertices and edges can be interesting objects of study. We look at the number of isosceles triangles where the vertices are points on a regular grid and show that they satisfy a recurrence relation when the grid is large enough. We also derive recurrence relations for the number of acute, obtuse and right isosceles triangles.
DOI:10.48550/arxiv.1605.00180