Dissertation (Ph.D.)--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references.

The purpose of this paper is the investigation of various properties of ordered triples whose components are elements of certain sets.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, August 2003. / Includes bibliographical references. Also available on the Internet.

This report expresses some of the recent research surrounding the Pythagorean Theorem and Pythagorean triples. Topics discussed include applications of the Pythagorean Theorem relating to recursion methods, acute and obtuse triangles, Pythagorean triangles in squares, as well as Pythagorean boxes. A short discussion on the depth of the Pythagorean Theorem taught in secondary schools is also included. / text

Thesis (Ph. D.)--West Virginia University, 1998. / Title from document title page. "September 10, 1998." Document formatted into pages; contains v, 85 p. : ill. Vita. Includes abstract. Includes bibliographical references (p. 79-82).

Abstract Not Provided. / Thesis / Master of Science (MSc)

Euclid’s Method of finding Pythagorean triples is a commonly accepted and applied technique. This study focuses on a myriad of other methods behind finding such Pythagorean triples. Specifically, we discover whether or not other ways of finding triples are special cases of Euclid’s Method.

Note: / Butler's Theorems, with one minor exception, are resolved: in a 2-categorical setting. His Adjointness theorems are all proved correct, after one tiny modification. Then, using a condition on adjoint squares, twenty-two of his Tripleability theorems are proved correct; th~ee are proved false. The other theorem is still unresolved, but it is of very minor importance. / Les theoremes de Butler, a l'exception d'un seul de peu d'importance, sont resulus dans un contexte 2-categorique.Tous ses theoremes d'adjonction sont demontres etre valides apres une modification minime. Ensuit~ utilisant une condition de carres adjoints, vingt-deux de ses Theoremes de monadicite sont demontres et trois autres sont refutes. La validation ou refutation d'un seul de ses +heoremes, de peu d'importance, demeure en suspense.

Butler's Theorems, with one minor exception, are resolved: in a 2-categorical setting. His Adjointness theorems are all proved correct, after one tiny modification. Then, using a condition on adjoint squares, twenty-two of his Tripleability theorems are proved correct; three are proved false. The other theorem is still unresolved, but it is of very minor importance.

Note: