See also:geometry, a closed
See also:curve, generally more or less
See also:egg-like in
See also:form . The simplest
See also:oval is the 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 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 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 Salmon, Higher
See also:Plane Curves .
SIR JAMES OUTRAM (1803—1863)
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