A thing of beauty is a joy for ever

• Autores: V.K. Srinivasan
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 43, Nº. 4, 2012, págs. 521-538
• Idioma: inglés
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• Resumen

  • Three unheralded results, two in Coordinate Geometry and the other in Plane Geometry, provide three proofs of a theorem dubbed by this author as �The Fundamental Theorem�. The above theorem offers a uniform proof establishing the positive integral nature of the radii of the incircle and the three escribed circles associated with the right triangle corresponding to any Pythagorean triplet of natural numbers. Another special selection of Pythagorean triplet ensures the positive integral nature of the radii of six circles namely; the incircle, circumscribing circle, the three escribed circles and the nine point circle of the right triangle that comes from the specialized Pythagorean triplet. Through these connections some other new results that can be deduced from the Pythagorean triplet are presented in this article.