%0 Journal Article %T Torsion in Groups of Integral Triangles %A Will Murray %J Advances in Pure Mathematics %P 116-120 %@ 2160-0384 %D 2013 %I Scientific Research Publishing %R 10.4236/apm.2013.31015 %X

Let 0£¼¦Ã£¼¦Ð 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 ¦Ã. Addition in Hr is defined by adding the angles ¦Â opposite side b and modding out by ¦Ð-¦Ã. The only Hr for which the structure is known is H¦Ð/2, which is free abelian. We prove that for general¦Ã, Hr has an element of order two iff 2(1- %K Abelian Groups %K Cubic Equations %K Examples %K Free Abelian %K Geometric Constructions %K Group Theory %K Integral Triangles %K Law of Cosines %K Primitive %K Pythagorean Angles %K Pythagorean Triangles %K Pythagorean Triples %K Rational Squares %K Three-Torsion %K Torsion %K Torsion-Free %K Two-Torsion %K Triangle Geometry %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=27375