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Topic: Ellipse

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In the News (Thu 23 May 19)

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.
The pedal of a ellipse with respect to a focus is a circle, conversely, the negative pedal of a circle with respect to a point inside the circle is a ellipse.
Ellipse's inversion with respect to a focus is a dimpled limacon of Pascal.
xahlee.org /SpecialPlaneCurves_dir/Ellipse_dir/ellipse.html   (1425 words)

  Ellipse - MSN Encarta
The ellipse is used in engineering in the arches of some bridges and the design of gears for certain types of machinery such as Wankel engines and punch presses.
Ellipses are also symmetrical with respect to their minor axes, lines perpendicular to the major axis at the midpoint between the two foci.
Ellipses are a type of conic section, a class of curves formed by a plane that cuts through a right circular cone.
encarta.msn.com /encyclopedia_761567895/Ellipse.html   (485 words)

  Ellipse - Wikipedia, the free encyclopedia
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.
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.
The shape of an ellipse is usually expressed by a number called the eccentricity of the ellipse, conventionally denoted e (not to be confused with the mathematical constant e).
en.wikipedia.org /wiki/Ellipse   (1474 words)

 Ellipse -- from Wolfram MathWorld
The ellipse is a conic section and a Lissajous curve.
is a characteristic of the ellipse known as the eccentricity, to be defined shortly.
Furthermore, the eccentricities of the ellipse and hyperbola are reciprocals.
mathworld.wolfram.com /Ellipse.html   (1252 words)

Kepler, in 1602, 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.
The pedal curve of an ellipse, with its focus as pedal point, is a circle.
The evolute of the ellipse with equation given above is the Lamé curve.
www-groups.dcs.st-and.ac.uk /~history/Curves/Ellipse.html   (238 words)

An ellipse can be represented parametrically by the equations x = a cos θ and y = b sin θ, where x and y are the rectangular coordinates of any point on the ellipse, and the parameter θ is the angle at the center measured from the x-axis anticlockwise.
Therefore, a normal to the ellipse is found by bisecting the angle between the radii to F and F', and a tangent is perpendicular to the normal.
The focal definition of an ellipse is that an ellipse is the locus of points the ratio of whose distances from a fixed line, the directrix, to a fixed point, the focus, is a constant e, called the eccentricity.
www.du.edu /~jcalvert/math/ellipse.htm   (5042 words)

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