Archimedes got an ellipse shrinking a circle along one direction. Then Archimedes could deduce the area of an ellipse as a generalization of the area of a circle.

An ellipse has two axes of symmetry that we call the major and the minor axes.

An ellipse is commonly defined as the locus of points P such that the sum of the distances from P to two fixed points F1, F2 (called foci) are constant.

This two foci lies on its major axis, at equal distances from the center of the ellipse.

In this page we can see (intuitively) how Archimedes' approach and this definition of an ellipse are the same.

We might use Pythagoras' theorem to calculate the position of these two foci.

From the definition, a point P in the ellipse verify:

A circle is a special case of an ellipse (when a = b). In this case the two foci points are just the same: the center of the circle.

LINKS

	Equation of an ellipse Transforming a circle we can get an ellipse (as Archimedes did to calculate its area). From the equation of a circle we can deduce the equation of an ellipse.
	Archimedes and the area of an ellipse: an intuitive approach In his book 'On Conoids and Spheroids', Archimedes calculated the area of an ellipse. We can see an intuitive approach to Archimedes' ideas.
	Archimedes and the area of an ellipse: Demonstration In his book 'On Conoids and Spheroids', Archimedes calculated the area of an ellipse. It si a good example of a rigorous proof using a double reductio ad absurdum.
	Plane developments of geometric bodies (4): Cylinders cut by an oblique plane We study different cylinders cut by an oblique plane. The section that we get is an ellipse.
	The Complex Cosine Function The Complex Cosine Function extends the Real Cosine Function to the complex plane. It is a periodic function that shares several properties with his real ancestor.