Everyone knows what an oval "is," at least in everyday terms. For many people, the image that springs to mind upon reference to an oval shape is the human eye. Fans of auto, horse, dog or human racing might think first of a paved or rubberized surface dedicated to contests of speed. Countless other examples of an oval image of course exist.

The "oval" as a mathematical concern, however, is a different beast. Most of the time, when people refer to an oval, they are referring to a regular geometric shape called an ellipse, even though the two aren't the same. Confused? Keep reading.

## Oval: Definition

As you may have gathered from the discussion above, "oval" is not a term with a strict mathematical or geometric definition, and is no more formal or specific than "tapered" or "pointed." An oval is best regarded as a *convex* (that is, outward-curving, as opposed to *concave*) closed curve that may or may not display symmetry along one or both axes. The word is derived from the Latin *ovum*, which means "egg."

Oval dimensions are not always amenable to geometric calculations, but the dimensions of ellipses always are. Perhaps the easiest way to think about it is that all ellipses are ovals, but not all ovals are ellipses. Taking things a step further, all circles are also ellipses, but are rarely described as such for fairly obvious reasons.

## The Ellipse vs. the Oval

An ellipse resembles a circle that has been flattened by applying a weight from above precisely to the center of the circle, causing it to be compressed equally to the left and the right. This means that if you draw a vertical line through the middle of the ellipse, you get two equal halves, and that the same thing happens if you draw a horizontal line through its center.

Another way to express this information is to say that an ellipse has two diameters at right angles to each other. These two lines are called the **major axis** (the "length" of the ellipse) and the **minor axis** (the "width"). Any line drawn from one side of the ellipse to the other is considered a diameter; the major axis and the minor axis are the longest and shortest of the possibilities respectively.

## The Geometry and Algebra of Ellipses

The standard form of the equation of an ellipse is:

where *a* and *b* are the lengths of the axes and the ellipse has been plotted on a set of standard coordinates with its center at (0, 0), that is, at *x* = 0 and *y* = 0. An ellipse can also be described by an equation of the form

where the capital letters (coefficients) are constants, provided *B*^{2} − 4_AC_ (the "discriminant") has a negative value.

You may not have occasion to put all of these points into play in your studies, but thinking about the world geometrically is rarely a losing proposition, as it teaches you to conceive of massive objects interacting in a way that can be wholly specified by mathematics.

## Planetary Orbits

Ellipses, and by extension ovals, are perhaps nowhere more important than in the realm of astrophysics. You may have learned or passively assumed that the orbits of planets, moons and comets are circular, but in fact they are all elliptical to varying degrees.

Eccentricity (*e*) is a property of ellipses that describe how "un-circular" they are, with higher values signifying a "flatter" shape. That of Earth is 0.02, with those of six of the remaining seven planets ranging from 0.01 to 0.09. Only Mercury, with an e value of 0.21, is an "outlier" among the planets. Comets, on the other hand, can have wildly eccentric orbits.

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#### Photo Credits

- oval mirror illustration image by robert mobley from Fotolia.com