A fresh approach to generating Pythagorean triples

• Main Authors: Andal, Don Perry, Park, Ji Hyun
• Format: text
• Language: English
• Published: Animo Repository 2021
• Subjects: Pythagorean theorem; Number theory; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/5028
• Institution: De La Salle University

One way of generating a Pythagorean triple is by the Euclidean formula. However, the Euclidean Formula cannot generate all of the triples. One example is the triple (9, 12, 15). This triple cannot be generated by the Euclidean formula unless we use a multiplier to a triple which can be generated by the Euclidean formula unless we use a multiplier to a triple which can be generated by the Euclidean formula, in this case, (3, 4, 5). Another example is the triple (4, 3, 5). To generate this triple, one must physically interchange the first and the second component of the triple (3, 4, 5). This thesis explains a new formula of generating triples from the article Rethinking Pythagorean Triples by William Spezeski which generates all of the Pythagorean triples without using multipliers and transposition.