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An epicycloid with n=5 cusps, named after the buttercup genus Ranunculus (Madachy 1979). Its parametric equations are x = a[6cost-cos(6t)] (1) y = a[6sint-sin(6t)]. (2) Its ...

A polynomial having only real numbers as coefficients. A polynomial with real coefficients is a product of irreducible polynomials of first and second degrees.

Given a rectangle BCDE, draw EF=DE on an extension of BE. Bisect BF and call the midpoint G. Now draw a semicircle centered at G, and construct the extension of ED which ...

Specifying two sides and the angle between them uniquely (up to geometric congruence) determines a triangle. Let c be the base length and h be the height. Then the area is ...

In any triangle, the locus of a point whose pedal triangle has a constant Brocard angle and is described in a given direction is a circle of the Schoute coaxal system.

For p(z)=a_nz^n+a_(n-1)z^(n-1)+...+a_0, (1) polynomial of degree n>=1, the Schur transform is defined by the (n-1)-degree polynomial Tp(z) = a^__0p(z)-a_np^*(z) (2) = ...

A translation along a straight line L and a rotation about L such that the angle of rotation is proportional to the translation at each instant. Also known as a twist.

The number of operations needed to effect a geometric construction as determined in geometrography. If the number of operations of the five geometrographic types are denoted ...

Sinai billiards is the reflection of a ray of light by an arrangement of perfectly reflecting circles in the plane (Trott 2004, pp. 28-30). The path is extremely sensitive to ...

The tangent indicatrix of a curve of constant precession is a spherical helix. The equation of a spherical helix on a sphere with radius r making an angle theta with the ...