Online Encyclopedia

Search over 40,000 articles from the original, classic Encyclopedia Britannica, 11th Edition.

OVAL (Lat. ovum, egg)

Online Encyclopedia
Originally appearing in Volume V20, Page 382 of the 1911 Encyclopedia Britannica.
» Make a correction to this article.
» Add information or comments to this article.
Spread the word: del.icio.us del.icio.us it!

See also:

OVAL (See also:Lat. ovum, See also:egg) , in See also:geometry, a closed See also:curve, generally more or less egg-like in See also:form. The simplest oval is the See also:ellipse; more complicated forms are represented in the notation of See also:analytical geometry by equations of the 4th, 6th, 8th . . . degrees. Those of the 4th degree, known as bicircular quartics, See also:ate the most important, and of these the See also:special forms named after See also:Descartes and See also:Cassini are of most See also:interest. The Cartesian ovals presented themselves in an investigation of the See also:section of a See also:surface which would refract rays proceeding from a point in a See also:medium of one refractive See also:index into a point in a medium of a different refractive index. The most convenient See also:equation is lrtmr' =n, where r,r' are the distances of a point on the curve from two fixed and given points, termed the foci, and 1, m, n are constants. The curve is obviously symmetrical about the See also:line joining the foci, and has the important 'See also:property that the normal at any point divides the See also:angle between the radii into segments whose sines are in the ratio 1: m. The Cassinian oval has the equation rr' = See also:a2, where r,r' are the radii of a point on the curve from two given foci, and a is a See also:constant. This curve issymmetrical 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 See also:Bernoulli's ler lniscate (q.v.). See CURVE; also See also:Salmon, Higher See also:Plane Curves.

End of Article: OVAL (Lat. ovum, egg)

Additional information and Comments

There are no comments yet for this article.
» Add information or comments to this article.
Please link directly to this article:
Highlight the code below, right click, and select "copy." Then paste it into your website, email, or other HTML.
Site content, images, and layout Copyright © 2006 - Net Industries, worldwide.
Do not copy, download, transfer, or otherwise replicate the site content in whole or in part.

Links to articles and home page are always encouraged.

[back]
OUTRAM, SIR JAMES (1803—1863) 		[next]
OVAR

Site © 2006 - Net Industries