Pi is not Constant: Exploring π in Non-Euclidean Spaces
2025-09-15
This article explores the value of pi (π) in various metric spaces. By altering the distance formula in Euclidean geometry, a series of non-Euclidean spaces are constructed, and the ratio of circumference to diameter of 'circles' in these spaces is calculated. The results show that while in standard Euclidean space (n=2), π is approximately 3.14159, its value changes in other spaces. For instance, in taxicab geometry (n=1) and Chebyshev distance (n→∞), π equals 4. This demonstrates that π's value isn't constant but depends on the underlying geometry of the space.