The high-accuracy geometric approximation of the ellipse's perimeter by the measuring right-angled triangle

Al-ossmi, Laith H. M.

Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika
Vol 7 No 2 (2025): Alifmatika - December

This article confronts the persistent challenge of determining the exact perimeter of an ellipse. It proposes a high-accuracy geometric approximation centred on a uniquely defined Measuring Right-Angled Triangle (MRAT). Constructed with specific spatial and angular properties, the MRAT is positioned at a distance of 2b/π from the centre of a reference circle and terminates at its circumference at a 45° angle. The ellipse's center is co-located with the circle's center. The resulting values were rigorously compared against classical Ramanujan approximations, and the PRI test and high-precision graphical analysis were used to confirm significant accuracy. This high-accuracy geometric approximation method offers a computationally efficient alternative to traditional algebraic methods, enhancing both theoretical understanding and applied precision.