Beyond π: A Mixed Rational Formula Delivering 20-Decimal Precision for Circle Circumference

This work introduces an original formula to approximate the circumference of a circle without direct reliance on the constant π. The method combines a mixed rational expression with a fractional correction factor. For a circle of radius 1, the final formula achieves numerical precision up to 20 decimal places compared to the exact value 2π. The approach provides a simple, closed-form expression suitable for both theoretical exploration and practical computation, offering an alternative path to high-precision perimeter calculation without iterative methods or floating-point dependencies.