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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 ...

A stellation is said to be fully supported if all its included cells are supported, i.e., if all its bottom faces are covered by their adjacent cells. In other words, every ...

A perspective collineation with center O and axis o not incident is called a geometric homology. A geometric homology is said to be harmonic if the points A and A^' on a line ...

A function which satisfies f(tx,ty)=t^nf(x,y) for a fixed n. Means, the Weierstrass elliptic function, and triangle center functions are homogeneous functions. A ...

The pedal curve of a rectangular hyperbola with the pedal point at the focus is a circle (left figure; Hilbert and Cohn-Vossen 1999, p. 26). The pedal curve of a rectangular ...

A two-dimensional planar closed surface L which has a mass M and a surface density sigma(x,y) (in units of mass per areas squared) such that M=int_Lsigma(x,y)dxdy. The center ...

A line along a normal vector (i.e., perpendicular to some tangent line). If K subset R^d is a centrosymmetric set which has a twice differentiable boundary, then there are ...

A tree is planted at each lattice point in a circular orchard which has center at the origin and radius r. If the radius of trees exceeds 1/r units, one is unable to see out ...

The centroid of the four points constituting an orthocentric system is the center of the common nine-point circle (Johnson 1929, p. 249). This fact automatically guarantees ...

All Euclidean geometric constructions can be carried out with a straightedge alone if, in addition, one is given the radius of a single circle and its center. The theorem was ...