Abstract
In this chapter we study properties of integer triangles. We start with the sine formula for integer triangles. Then we introduce integer analogues of classical Euclidean criteria for congruence for triangles and present several examples. Further, we verify which triples of angles can be taken as angles of an integer triangle; this generalizes the Euclidean condition α+β+γ=π for the angles of a triangle (this formula will be used later in Chap. 13 to study toric singularities). Then we exhibit trigonometric relations for angles of integer triangles. Finally, we give examples of integer triangles with small area.
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© 2013 Springer-Verlag Berlin Heidelberg
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Karpenkov, O. (2013). Integer Angles of Integer Triangles. In: Geometry of Continued Fractions. Algorithms and Computation in Mathematics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39368-6_6
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DOI: https://doi.org/10.1007/978-3-642-39368-6_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39367-9
Online ISBN: 978-3-642-39368-6
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