If Mathematics Were Base 7, Pi = 22/7 = 3.1 (Base 7) Would Be Rational

In a geometric system grounded in base 7 arithmetic, pi is redefined as the rational number 22/7 = 3.1 (in base 7), emerging as a direct consequence of the system’s internal logic rather than as an approximation. Using a full circle of 121 (base 7) = 64 (decimal) units and a quarter circle of 22 (base 7) = 16 (decimal), the model ensures integer divisions and rational values for perimeters, areas, and trigonometric calculations. Unlike the classical transcendental pi, this rational value integrates naturally within base 7 arithmetic. The paper explores the structural reasons for this redefinition and reveals connections to prime number patterns in base 7, suggesting a deeper arithmetic-geometric coherence.