Saturday, 12 August 2006



Taken in Melbourne University Baillieu. This was the stairs which I decided to shoot when we were having break.

In mathematics, an ellipse (from the Greek for absence) is the locus of points on a plane where the sum of the distances from any point on the curve to two fixed points is constant. The two fixed points are called foci (plural of focus).


An ellipse is a type of conic section: if a conical surface is cut with a plane which does not intersect the cone's base, the intersection of the cone and plane is an ellipse. For a short elementary proof of this, see Dandelin spheres.

Algebraically, an ellipse is a curve in the Cartesian plane defined by an equation of the form

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

such that B2 <>, where all of the coefficients are real, and where more than one solution, defining a pair of points (x, y) on the ellipse, exists.

An ellipse can be drawn with two pins, a loop of string, and a pencil. The pins are placed at the foci and the pins and pencil are enclosed inside the string. The pencil is placed on the paper inside the string, so the string is taut. The string will form a triangle. If the pencil is moved around so that the string stays taut, the sum of the distances from the pencil to the pins will remain constant, satisfying the definition of an ellipse.

No comments: