Plane figure · Circles
Ellipse
A circle stretched in one direction: the set of points whose distances to two foci add to 2a.
Dimensions
Results
Formulas
Stretching a circle of radius b by a/b in one direction multiplies every area by a/b: πb² · a/b = πab. The perimeter has no formula in elementary functions; Ramanujan’s (1914) is good to a few parts per million for ordinary shapes.
Older handbooks give P ≈ π√(2(a² + b²)), which overestimates: by about 2.5 % when one axis is twice the other, and more for flatter ellipses.
Checked: the A formula agrees with a Monte Carlo measurement of the shape itself, made from its geometric definition, every time the site is built.
Topologically a disc, like every figure here without a hole: Euler characteristic 1. Stretching turns it into a circle, a square or a star. More on the lens.