text: Main Entry: el·lipse \nPronunciation: i-'lips, e-\nFunction: noun\nEtymology: Greek elleipsis\n1 a : OVAL b : a closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points is a constant : a plane section of a right circular cone that is a closed curve\n\nSolar system woul;d be a good example of an elleipsis, the planets revolve around the sun, the fixed point.\n\nHow about the shape of a tanker truck, or the shape of the world itself. \n\nELLIPSE\n\nAlthough the circle is a very common shape, most of the time when we see a circle, it doesn't look like a circle! Because we usually see circles from an angle...and the shape then isn't perfectly round, it's another mathematical curve called an ellipse.One description of an ellipse is a squashed, stretched or otherwise distorted circle. \n\n\n \n\nAn ellipse can be seen as a slice of a cone, but it can also be seen when you tilt a glass partially filled with water or juice.\n\nUnlike a circle, whose shape never changes, there are many different shapes of ellipses: long narrow ones ... and rounder ones. \n\nDraftsmen have templates that enable them to draw the correct shape of ellipse for any use. We call the vertical and horizontal lines (shown in red below) the axes; the major axis is the longer of the two ... but it isn't necessarily the horizontal one.\n\n\n \n\nThe relationship between the major and minor axes determine the shape of the ellipse. The mathematician's word for shape is this case is eccentricity, and refers to the curvature. It is closely related to the ratio between the lengths of the two axes ... If the major and minor axes are equal, the ellipse is a circle. Shall we define an ellipse as a distorted circle, then, or the circle as a special case of the ellipse? Either one would be reasonable and useful.\n\nThe shape of the ellipse makes it more useful in some instances than the circle: since it is longer than it is wide it forms a comfortable shape for your hand ... It is a stable shape: a tank truck is in the shape of an ellipse. If it were circular, it would be taller than it is wide and then be top-heavy. A circle would have given it a larger capacity however, for the circle has the greatest area for a given perimeter, and is therefore the most economical container.\n\n\n\n\nAnother way of defining an ellipse is as one of four curves called The Conics, that can be cut from a cone. A, cone sliced parallel to the base has a circular cross-section, but if we angle the slice the result is an ellipse. Varying the angle changes the eccentricity of the ellipse. You will also get ellipses if you slice a cylinder.\n\n\n\n\nThe conical beam of light from a flashlight casts an elliptical pattern of light on the wall when held at an angle. If we move the point of the cone further away, an angled slice will still give us an ellipse: no matter how far we move the point of the cone. Imagine the point as far away as infinity...the cone becomes a cylinder and we still have an ellipse in cross-section.\n\nSalami is often cut in elliptical slices ... and tilting a glass of soda to drink with our salami would reveal yet another ellipse! Any cylinder sliced on an angle will reveal an ellipse in cross-section, such as seen in the Tycho Brahe Planetarium in Copenhagen:\n\n\n \n\n\nhttp://www.astro.ku.dk/~lars_c/tbp/tychoeng.html \n\nThe mathematical definition of an ellipse is the set of all points such that the sum of the distances from two fixed points is constant. The distance from any point of the ellipse to one focus plus the distance from that same point to the other focus is always the same number for a particular ellipse: seven in the example below. Two plus five equals seven ... three plus four equals seven ... three and one-half plus three and one-half equals seven.\n\n\n\n\nWe can use this definition to derive an equation for an ellipse with its center at the origin on a Cartesian coordinate sy