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Ellipses also arise as images of a circle or a sphere under parallel projection, and some cases of perspective projection. Indeed, circles are special cases of ellipses. An ellipse is also the closed and bounded case of an implicit curve of degree 2, and of a rational curve of degree 2. It is also the simplest Lissajous figure, formed when the horizontal and vertical motions are sinusoids with the same frequency.

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Wikipedia About Elliptical

Conicas1.PNG

Ellipses also arise as images of a circle or a sphere under parallel projection, and some cases of perspective projection. Indeed, circles are special cases of ellipses. An ellipse is also the closed and bounded case of an implicit curve of degree 2, and of a rational curve of degree 2. It is also the simplest Lissajous figure, formed when the horizontal and vertical motions are sinusoids with the same frequency.

Elements of an ellipse

An ellipse is a smooth closed curve which is symmetric about its center. The distance between antipodal points on the ellipse, or pairs of points whose midpoint is at the center of the ellipse, is maximum and minimum along two perpendicular directions, the major axis or transverse diameter, and the minor axis or conjugate diameter.

The semimajor axis (denoted by a in the figure) and the semiminor axis (denoted by b in the figure) are one half of the major and minor diameters, respectively. These are sometimes called (especially in technical fields) the major and minor semi-axes,, the major and minor semiaxes, or major radius and minor radius. When a and b are equal, the foci coincide with the center, and the ellipse becomes a circle with radius a=b.

There are two special points F1 and F2 on the ellipse's major axis, on either side of the center, such that the sum of the distances from any point of the ellipse to those two points is constant and equal to the major diameter (2 a). Each of these two points is called a focus of the ellipse.

The eccentricity of an ellipse, usually denoted by ε or e, is the ratio of the distance between the foci to the length of the major axis. The eccentricity is necessarily between 0 and 1; it is zero if and only if a=b, in which case the ellipse is a circle. The distance ae from a focal point to the centre is called the linear eccentricity of the ellipse.

The pins-and-string method

Drawing%20an%20ellipse%20via%20two%20tacks%20a%20loop%20and%20a%20pen.jpg

An ellipse can be drawn using two pins, a length of string, and a pencil:

Push the pins into the paper at two points, which will become the ellipse's foci. Tie the string into a loose loop around the two pins. Pull the loop taut with the pencil's tip, so as to form a triangle. Move the pencil around, while keeping the string taut, and its tip will trace out an ellipse.

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Ellipse - Wikipedia, the free encyclopedia

3.1 Elliptical reflectors and acoustics. 3.2 Planetary orbits. 3.3 Harmonic ... 3.5 Elliptical gears. 3.6 Optics. 4 Mathematical definitions and properties ...en.wikipedia.org/wiki/Ellipse

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Londonist"All you Olympic sceptics will be Olympic maniacs by 2013." Booo. "No we won't!" Cheers. "Oh, I am confident you will." Booo. Cheers. Such was the lively, almost pantomime atmosphere at the 9th State of London debate , which took place at the QEII conference centre on Saturday. Hundreds of Londoners packed into the hall to quiz the mayor about his first year, and the untold joys his continuing ...http://londonist.com/2009/05/state_of_london_debate_2009.php

This week's Hubble upgrade to give UCI a 'huge lift'

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Low-angle Collision With Earth: The Elliptical Impact Crater Matt ...

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Prime Retail Incorporated

Chicago TribuneIn the grand space of what was long ago a bank, and not so long ago a health club, there are rows of dusty, unused treadmills, elliptical cross-trainers, stair-climbers and weight machines, a reminder of just how much our national mission has changedhttp://www.chicagotribune.com/topic/economy-business-finance...

Weight Watchers, gym help dieter exceed 40-pound goal

USA TodayAt first, she did the elliptical machine and treadmill. "I was the big girl at the back who wore baggy clothes. I didn't want to talk to anybody or be seen." After a few months, she started going to group fitness classes — aerobics, Pilates, yoga ... http://www.usatoday.com/news/health/weightloss/2009-05-10-ja...

Random snacking takes bite out of freelancer's goals

NewsdayDoes five minutes of weight machines with light resistance and 30 minutes on the elliptical trainer at level two (burning about 240 calories for her weight; the machine showed 262 calories, but some machines skew about 10% high). Bogart is sweating ... http://www.newsday.com/news/health/la-he-numbersher11-2009ma...

P. Diddy holds business meetings in the gym

AZCentral.comHe was huffing and puffing on the elliptical cross trainer with his cell phone glued to his ear. And he kept yelling at his assistants, 'You need to hustle! Try harder!' " Diddy is not the only star with a bizarre fitness regime. Madonna and her ... http://www.azcentral.com/ent/celeb/articles/2009/05/08/20090...

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Elliptical Trainers Ratings and Reviews

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Elliptical Machines

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Wikipedia results for Elliptical

Elliptical trainer - Wikipedia, the free encyclopedia

An elliptical trainer (also cross trainer or simply elliptical) is a stationary exercise machine used to simulate walking or running without causing excessive pressure to the ... http://en.wikipedia.org/wiki/Elliptical_trainer

Elliptical galaxy - Wikipedia, the free encyclopedia

An elliptical galaxy is a galaxy having an approximately ellipsoidal shape and a smooth, nearly featureless brightness profile. They range in shape from nearly spherical to highly ... http://en.wikipedia.org/wiki/Elliptical_galaxy

Ellipse - Wikipedia, the free encyclopedia

... pencil holder (point C) at one end, and two adjustable side pins (points A and B) that slide into two perpendicular slots cut into a a metal plate. Ellipses in physics Elliptical ... http://en.wikipedia.org/wiki/Ellipse

Ellipsis (linguistics) - Wikipedia, the free encyclopedia

In the grammar of a sentence, an ellipsis (from the Greek: ἔλλειψις, élleipsis, "omission") or elliptical construction is a construction that lacks an element that is ... http://en.wikipedia.org/wiki/Elliptical_construction

Elliptical wing - Wikipedia, the free encyclopedia

An elliptical wing is a wing planform shape, first seen on aircraft in the 1930s, which minimizes induced drag. [1] Elliptical taper shortens the chord near the wingtips in such a ... http://en.wikipedia.org/wiki/Elliptical_wing
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