The Ramanujan formula is a mathematical formula for approximating the perimeter of an ellipse, named after the famous Indian mathematician Srinivasa Ramanujan. It is given by:
P ≈ π(a + b) [ 3 - √(3a+b) - √(a+3b) ]
where P is the perimeter of the ellipse, a is the length of the semi-major axis, and b is the length of the semi-minor axis.
The Ramanujan formula provides a good approximation of the perimeter of an ellipse, with an error of less than 0.5% for most practical purposes. It is particularly useful for hand calculations and other situations where more exact methods may be impractical or time-consuming.
Some real-life applications of the perimeter of an ellipse include calculating the perimeter of racetracks, the outer boundaries of satellite orbits, and the perimeters of curved architectural features such as arches and domes.
