Search Results for ""

Fisheye perspective is a two-part projection. First, three-dimensional space is projected onto the surface of a hemisphere, by connecting every external point to the center ...

Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 in F_1 corresponds to P_0 in F_0 under the given similarity. Let r in (0,1), and define ...

If two single-valued continuous functions kappa(s) (curvature) and tau(s) (torsion) are given for s>0, then there exists exactly one space curve, determined except for ...

Two distinct knots cannot have the same exterior. Or, equivalently, a knot is completely determined by its knot exterior (Cipra 1988; Adams 1994, p. 261). The question was ...

Let a Gram point g_n be called "good" if (-1)^nZ(g_n)>0, and "bad" otherwise (Rosser et al. 1969; Edwards 2001, p. 180). Then the interval between two consecutive good Gram ...

Any one of the eight Apollonius circles of three given circles is tangent to a circle H known as a Hart circle, as are the other three Apollonius circles having (1) like ...

An optical illusion due to the physiologist Ewald Hering in 1861. The two horizontal lines are both straight, but they look as if they were bowed outwards. The distortion is ...

A regular two-dimensional arrangement of squares separated by vertical and horizontal "canals." Looking at the grid produces the illusion of gray spots in the white area ...

Pairs of points of a line, the product of whose distances from a fixed point is a given constant. This is more concisely defined as a projectivity of period two. If ...

Machin's formula is given by 1/4pi=4cot^(-1)5-cot^(-1)239. There are a whole class of Machin-like formulas with various numbers of terms (although only four such formulas ...