Triangle Area Numbers and Solid Rectangular Numbers

2008/03/31 by Konstantine D. Zelator, Zelator, Konstantine D.
Mathematics · #11A #A005 #FOS: Mathematics #General Mathematics (math.GM) #math.GM #msc:11A #msc:A005

paper · pdf · doi:10.48550/arxiv.0804.0010

22 pages

arxiv created 2008/03/31 · arxiv updated 2009/12/01

Abstract

In this work, we define a triangle area number to be the area number of a triangle whose sides have integer lengths, and whose area is a rational number. In Result 3, on page 17, we prove that every triangle area number is in fact an integer which is a multiple of 6. Certain divisibility and other conditions and formulas are also derived, which the three integer sidelengths must satisfy. On pages 20 and 21, we list all the triangle area numbers not exceeding 999.

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