MacTutorCurves
Ellipse
Description
The ellipse was first studied byMenaechmus.Euclid wrote about the ellipse and it was given its present name byApollonius. Thefocus anddirectrix of an ellipse were considered byPappus.Kepler, in1602, said he believed that the orbit of Mars was oval, then he later discovered that it was an ellipse with the sun at one focus. In factKepler introduced the word "focus" and published his discovery in1609. The eccentricity of the planetary orbits is small(i.e. they are close to circles). The eccentricity of Mars is1 /11 and of the Earth is1 /60 .
In1705Halley showed that the comet, which is now called after him, moved in an elliptical orbit round the sun. The eccentricity ofHalley's comet is0.9675 so it is close to a parabola(eccentricity1).
The area of the ellipse is. There is no exact formula for the length of an ellipse in elementary functions and this led to the study of elliptic functions.Ramanujan, in1914, gave the approximate length
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The pedal curve of an ellipse, with its focus as pedal point, is acircle.The evolute of the ellipse with equation given above is theLamé curve.
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From a point inside the evolute(it is a closed curve) four normals can be drawn to the ellipse but from a point outside only two normals can be drawn.Other Web site:
Xah Lee
