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Line 1: − An ellipse is a figure that looks like a squashed circle. The more squashed it is, the greater its [[eccentricity]]. − + + + + + + + + + + + Line 9:
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[[Image:658px-Elipse svg.png|right|thumb|400px|In the figure, ''a'' is the semi-major axis, ''b'' is the semi-minor axis, F1 and F2 are the two focal points. The distance F1-X-F2 is constant.]]
[[Image:658px-Elipse svg.png|right|thumb|400px|In the figure, ''a'' is the semi-major axis, ''b'' is the semi-minor axis, F1 and F2 are the two focal points. The distance F1-X-F2 is constant.]]
To draw an ellipse, place tacks at two points on a piece of paper with a string between them. Trace out the curve of the ellipse with a pencil which is always pushing against the string. The longer the string, the less eccentric the ellipse will be (and more circular).
An '''ellipse''' is a geometric figure that looks like a squashed [[circle]]. The more squashed it is, the greater its [[eccentricity]].
It is defined as the set of all points in a plane where the sum of the distance from two points, the ''foci'', is the same. A special case of the ellipse is the circle, where the two points are coincident.
To construct an ellipse, place tacks at two points on a piece of paper with a string between them. Trace out the curve of the ellipse with a pencil which is always pushing against the string. The longer the string, the less eccentric the ellipse will be (and more circular).
The general algebraic formula for an ellipse is given by:
:<math>ax^2 + bxy + cy^2 + dx + ey + f = 0</math>
An ellipse is a [[conic section]], the intersection of a plane and a cone, where the angle of the plane to the cone's axis is greater than the angle of the cone with its axis.
The terms ''eccentric'' and ''circular'' are antonyms.
The terms ''eccentric'' and ''circular'' are antonyms.
A whisper at one focal point is easily heard at the the other focal point, because the sound waves bounce off the walls and combine again at the other focal point.
A whisper at one focal point is easily heard at the the other focal point, because the sound waves bounce off the walls and combine again at the other focal point.
Ellipses became important in [[astronomy]] in the early 1600s, when [[Kepler]] proved that planets revolving the sun always follow elliptical [[orbit]]s. This helped overturn the [[Ptolemaic theory]], and led to [[Issac Newton]]'s [[law of gravitation]].
Ellipses became important in [[astronomy]] in the early 1600s, when [[Kepler]] proved that planets revolving the sun always follow elliptical [[orbit]]s, with the sun at one of the foci. This helped overturn the [[Ptolemaic theory]], and led to [[Issac Newton]]'s [[law of gravitation]].
[[category:geometry]]
[[category:geometry]]