The Ellipse Mean Radius calculator estimates Ellipse an average radius (rμ) of an ellipse based on the semi-major (a) and semi-minor (b) axes of the ellipse.
INSTRUCTIONS: Enter the following:
Ellipse Mean Radius (r): The calculator returns the mean radius (rμ) the same units as the axes.
In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a special type of an ellipse having both focal points at the same location. The shape of an ellipse (how "elongated" it is) is represented by its, which for an ellipse can be any number from 0 (the limiting case of a circle to arbitrarily close to but less than 1.
This formula uses the average of 200 measurements of the radius based on the definition of an ellipse:
` x^2/a^2 + y^2/b^2 = 1`
This algorithm computes the average of the radius based on 100 computations based on an x value from -a to a, where y is computed and 100 computations based on a y value from -b to b. For each, the distance from the origin is computed
`d = sqrt(x^2+ y^2)`
... and the arithematic mean is returned.
Description of an ellipse is from Wikipedia (en.wikipedia.org/wiki/Ellipse)