Number Theory

    

Parabolic Patterns in the Scatter Plot of Pythagorean Triples

Authors: Kuan Peng

The scatter plot of Pythagorean triples exhibits distinct parabolic patterns whose origins have not been fully characterized. In this work, we derive explicit parabolic functions directly from the Pythagorean equation and demonstrate their correspondence with these patterns. The analysis shows that basic Pythagorean triples are regularly distributed on the (X,Y) plane, occurring precisely at the intersections of horizontal and vertical parabolas. The derived functions align closely with the observed parabolic structures, and a density analysis of the parabolas explains the prominence of these patterns in the scatter plot of all Pythagorean triples.

Comments: 9 Pages. (Note by viXra Admin: Please cite and list scientific references)

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[v1] 2025-08-16 20:54:00

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