The high-accuracy geometric approximation of the ellipse's perimeter by the measuring right-angled triangle
DOI:
https://doi.org/10.35316/alifmatika.2025.v7i2.310-331Keywords:
Conic Sections, Ellipse Perimeter, Geometric Approximation, Ramanujan's ApproximationsAbstract
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.
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