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Theorem on a Matrix of Right-Angled Triangles
Applied and Computational Mathematics
Volume 2, Issue 2, April 2013, Pages: 36-41
Received: Mar. 11, 2013; Published: Apr. 2, 2013
Author
Martin W. Bredenkamp, Department of Science, Asia-Pacific International University; PO Box 4, MuakLek, Saraburi Province, 18180, Thailand
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Abstract
The following theorem is proved: All primitive right-angled triangles (primitive Pythagorean triples) may be defined by a pair of positive integer indices (i,j), where i is an uneven number and j is an even number and have no com-mon factor. The sides of every positive integer right angled triangle are then defined by the indices as follows: For hy-potenuse h, uneven leg u and even leg e, h = i2 + ij + j2/2, e = ij + j2/2, u = i2 + ij. This defines an infinite by infinite matrix of right angled triangles with positive integer sides.
Keywords
Primitive Right-Angled Triangles, Pythagorean Triples, Infinite Two-Dimensional Matrix
Martin W. Bredenkamp, Theorem on a Matrix of Right-Angled Triangles, Applied and Computational Mathematics. Vol. 2, No. 2, 2013, pp. 36-41. doi: 10.11648/j.acm.20130202.14
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