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An isoptic curve formed from the locus of tangents meeting at right angles. The orthoptic of a parabola is its conic section directrix. The orthoptic of a central conic was ...

The arc length of the parabolic segment y=h(1-(x^2)/(a^2)) (1) illustrated above is given by s = int_(-a)^asqrt(1+y^('2))dx (2) = 2int_0^asqrt(1+y^('2))dx (3) = ...

The circum-medial triangle DeltaA^'B^'C^' is the circumcevian triangle of a reference triangle DeltaABC with respect to the triangle centroid G of DeltaABC (Kimberling 1998, ...

The catacaustic of the Tschirnhausen cubic with parametric representation x = 3(t^2-3) (1) y = t(t^2-3) (2) with radiant point at (-8,0) is the semicubical parabola with ...

Curves with Cartesian equation ay^2=x(x^2-2bx+c) with a>0. The above equation represents the third class of Newton's classification of cubic curves, which Newton divided into ...

A plane curve is a curve that lies in a single plane. A plane curve may be closed or open. Curves which are interesting for some reason and whose properties have therefore ...

For a given curve C, consider the locus of the point P from where the tangents from P to C meet at a fixed given angle. This is called an isoptic curve of the given curve. ...

The reciprocal curve of a given circle is the locus of a point which moves so that its distance from the center of reciprocation varies as its distance from the line which is ...

An unduloid, also called an onduloid, is a surface of revolution with constant nonzero mean curvature. It is a roulette obtained from the path described by the foci of a ...

A quantity defined for a conic section which can be given in terms of semimajor a and semiminor axes b. interval curve e e=0 circle 0 0<e<1 ellipse sqrt(1-(b^2)/(a^2)) e=1 ...