In technical drawing an oval (from Latin ovum, 'egg') is a figure constructed from two pairs of arcs, with two different radii (see image on the right). The arcs are joined at a point, in which lines tangential to both joining arcs lie on the same line, thus making the joint smooth. Any point of an oval belongs to an arc with a constant radius (shorter or longer), whereas in an ellipse the radius is continuously changing.
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In geometry, an oval or ovoid is any curve resembling an egg or an ellipse, but not an ellipse. Unlike other curves, the term 'oval' is not welldefined and many distinct curves are commonly called ovals. These curves have in common that:
The word ovoidal refers to the characteristic of being an ovoid. An ovoid is the surface generated by rotating an oval curve about one of its axes of symmetry.
Other examples of ovals described elsewhere include:
The shape of an egg is approximately that of half each a prolate (long) and roughly spherical (potentially even slightly oblate/short) ellipsoid joined at the equator, sharing a principal axis of rotational symmetry, as illustrated above. Although the term eggshaped usually implies a lack of reflection symmetry across the equatorial plane, it may also refer to true prolate ellipsoids. It can also be used to describe the 2dimensional figure that, revolved around its major axis, produces the 3dimensional surface.
In the theory of projective planes, oval is used to mean a set of q + 1 points in PG(2,q) with no 3 on any line, the projective plane over the finite field with q elements. See oval (projective plane).
In common speech 'oval' means a shape rather like an egg or an ellipse, and it may be twodimensional or threedimensional. It also often refers to a figure that resembles two semicircles joined by a rectangle, like a cricket infield or oval racing track. Sometimes it can even refer to any rectangle with rounded corners.
The oval was applied to the Pennsylvania Railroad's freight locomotives. All freight steam locomotives on the Pennsylvania Railroad had oval number plates whilst the passenger and mixed traffic steam locomotives had keystone number plates.
OVAL (Lat. ovum, egg), in geometry, a closed curve, generally more or less egglike in form. The simplest oval is the ellipse; more complicated forms are represented in the notation of analytical geometry by equations of the 4th, 6th, 8th. .. degrees. Those of the 4th degree, known as bicircular quartics, are the most important, and of these the special forms named after Descartes and Cassini are of most interest. The Cartesian ovals presented themselves in an investigation of the section of a surface which would refract rays proceeding from a point in a medium of one refractive index into a point in a medium of a different refractive index. The most convenient equation is lr? mr' = n, where r,r are the distances of a point on the curve from two fixed and given points, termed the foci, and 1, n are constants. The curve is obviously symmetrical about the line joining the foci, and has the important property that the normal at any point divides the angle between the radii into segments whose sines are in the ratio 1: m. The Cassinian oval has the equation y r' = a 2 , where r,r are the radii of a point on the curve from two given foci, and a is a constant. This curve is symmetrical about two perpendicular axes. It may consist of a single closed curve or of two curves, according to the value of a; the transition between the two types being a figure of 8, better known as Bernoulli's lemniscate.
See CURVE; also Salmon, Higher Plane Curves.
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