Torsion in Groups of Integral Triangles

Affiliation(s)

Department of Mathematics and Statistics, California State University, Long Beach, USA.

Department of Mathematics and Statistics, California State University, Long Beach, USA.

ABSTRACT

Let 0＜*γ*＜π be a fixed pythagorean angle. We study the abelian group *H _{r}* of primitive integral triangles (

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

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

Cite this paper

W. Murray, "Torsion in Groups of Integral Triangles,"*Advances in Pure Mathematics*, Vol. 3 No. 1, 2013, pp. 116-120. doi: 10.4236/apm.2013.31015.

W. Murray, "Torsion in Groups of Integral Triangles,"

References

[1] O. Taussky, “Sums of Squares,” American Mathematical Monthly, Vol. 77, No. 8, 1970, pp. 805-830. doi:10.2307/2317016

[2] E. J. Eckert, “The Group of Primitive Pythagorean Triangles,” Mathematics Magazine, Vol. 57, No. 1, 1984, pp. 22-27. doi:10.2307/2690291

[3] J. Mariani, “The Group of the Pythagorean Numbers”, American Mathematical Monthly, Vol. 69, 1962, pp. 125-128. doi:10.2307/2312540

[4] B. H. Margolius, “Plouffe’s Constant is Transcendental,” http://www.plouffe.fr/simon/articles/plouffe.pdf.

[5] E. J. Eckert and P. D. Vestergaard, “Groups of Integral Triangles,” Fibonacci Quarterly, Vol. 27, No. 5, 1989, pp. 458-464.

[1] O. Taussky, “Sums of Squares,” American Mathematical Monthly, Vol. 77, No. 8, 1970, pp. 805-830. doi:10.2307/2317016

[2] E. J. Eckert, “The Group of Primitive Pythagorean Triangles,” Mathematics Magazine, Vol. 57, No. 1, 1984, pp. 22-27. doi:10.2307/2690291

[3] J. Mariani, “The Group of the Pythagorean Numbers”, American Mathematical Monthly, Vol. 69, 1962, pp. 125-128. doi:10.2307/2312540

[4] B. H. Margolius, “Plouffe’s Constant is Transcendental,” http://www.plouffe.fr/simon/articles/plouffe.pdf.

[5] E. J. Eckert and P. D. Vestergaard, “Groups of Integral Triangles,” Fibonacci Quarterly, Vol. 27, No. 5, 1989, pp. 458-464.