Pythagorean Triples and the Circle
Year: 2026
Type: preprint
Abstract: The universal limit arising from all Pythagorean triples, when multiplied by the right angle, yields the circle: We prove that primitive Pythagorean triples encode the circle in their universal limit. For any sequence of primitive Pythagorean triples with governing parameter n = 2a/(c−b) → ∞, the product nθ converges to 4, where θ is the smaller acute angle measured in radians. This limiting value of 4, if read as an angle in radians, equals 720°/π = 229.183118052°. Together with the elementary observation that 4 × π/2 = 2π, this reframes the value 4 obtained from the triple limit as the natural link between the discrete geometry of integer right triangles and the continuous geometry of the circle.
Author: Rajput, Chetansing
Language: English
Topic: Mathematics and Applications
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7172519523
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