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The Maclaurin trisectrix is a curve first studied by Colin Maclaurin in 1742. It was studied to provide a solution to one of the geometric problems of antiquity, in ...

The pedal curve of the parabola with parametric equations x = at^2 (1) y = 2at (2) with pedal point (x_0,y_0) is x_p = ((x_0-a)t^2+y_0t)/(t^2+1) (3) y_p = ...

A polygonal number of the form n(3n-1)/2. The first few are 1, 5, 12, 22, 35, 51, 70, ... (OEIS A000326). The generating function for the pentagonal numbers is ...

Plücker's conoid is a ruled surface sometimes also called the cylindroid, conical wedge, or conocuneus of Wallis. von Seggern (1993, p. 288) gives the general functional form ...

If p and q are distinct odd primes, then the quadratic reciprocity theorem states that the congruences x^2=q (mod p) x^2=p (mod q) (1) are both solvable or both unsolvable ...

The term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two equal circles whose centers are offset ...

The radial curve of the catenary x = t (1) y = cosht (2) with radiant point (x_0,y_0) is given by x_r = x_0-coshtsinht (3) y_r = y_0+cosht. (4)

The system of partial differential equations u_t = 3ww_x (1) w_t = 2w_(xxx)+2uw_x+u_xw. (2)

The second-order ordinary differential equation (1+x^2)^2y^('')+lambday=0 (Hille 1969, p. 357; Zwillinger 1997, p. 122).

The base-26 number system composed of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and the letters A-P.