On the Curved Patterns Seen in the Graph of PPTs
James M. Parks
TL;DR
This paper investigates the patterns formed by primitive Pythagorean triples with small legs, revealing that their graphical representation follows parabolic curves explained through mathematical analysis.
Contribution
The paper demonstrates that the observed patterns in PPT graphs are parabolas, providing a mathematical explanation for these visually intriguing patterns.
Findings
The PPTs form parabolic curves in the graph.
Mathematical analysis explains the origin of these parabolas.
Patterns are consistent across different ranges of PPTs.
Abstract
Dr. Ron Knott constructed a graph of all Primitive Pythagorean Triples (PPTs) with legs up to length 10,000, using Mathematica. The patterns are very interesting, suggesting conic sections. We show that they indeed are parabolic curves which follow in a natural way from the mathematics of the subject matter.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · Advanced Theoretical and Applied Studies in Material Sciences and Geometry