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If two projective pencils of curves of orders n and n^' have no common curve, the locus of the intersections of corresponding curves of the two is a curve of order n+n^' ...

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...

The winding number of a contour gamma about a point z_0, denoted n(gamma,z_0), is defined by n(gamma,z_0)=1/(2pii)∮_gamma(dz)/(z-z_0) and gives the number of times gamma ...

The cornoid is the curve illustrated above given by the parametric equations x = acost(1-2sin^2t) (1) y = asint(1+2cos^2t), (2) where a>0. It is a sextic algebraic curve with ...

The term diamond is another word for a rhombus. The term is also used to denote a square tilted at a 45 degrees angle. The diamond shape is a special case of the superellipse ...

A strophoid of a circle with the pole O at the center of the circle and the fixed point P on the circumference of the circle. Freeth (1878, pp. 130 and 228) described this ...

The Gosper island (Mandelbrot 1977), also known as a flowsnake (Gardner 1989, p. 41), is a fractal that is a modification of the Koch snowflake. The term "Gosper island" was ...

A hypotrochoid is a roulette traced by a point P attached to a circle of radius b rolling around the inside of a fixed circle of radius a, where P is a distance h from the ...

The isoperimetric quotient of a closed curve is defined as the ratio of the curve area to the area of a circle (A=pir_A^2) with same perimeter (p=2pir_p) as the curve, Q = ...

A fractal derived from the Koch snowflake. The base curve and motif for the fractal are illustrated below. The area enclosed by pieces of the curve after the nth iteration is ...