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Torsion in Groups of Integral Triangles

DOI: 10.4236/apm.2013.31015, PP. 116-120

Keywords: Abelian Groups, Cubic Equations, Examples, Free Abelian, Geometric Constructions, Group Theory, Integral Triangles, Law of Cosines, Primitive, Pythagorean Angles, Pythagorean Triangles, Pythagorean Triples, Rational Squares, Three-Torsion, Torsion, Torsion-Free, Two-Torsion, Triangle Geometry

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Abstract:

Let 0γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1-

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