全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

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

Full-Text   Cite this paper   Add to My Lib

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-

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.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133