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A homeomorphism, also called a continuous transformation, is an equivalence relation and one-to-one correspondence between points in two geometric figures or topological ...

The hyperbolic polar sine is a function of an n-dimensional simplex in hyperbolic space. It is analogous to the polar sine of an n-dimensional simplex in elliptic or ...

A polyhedron in a hyperbolic geometry.

Given a triangle DeltaA_1A_2A_3, the points A_1, I, and J_1 lie on a line, where I is the incenter and J_1 is the excenter corresponding to A_1. Furthermore, the circle with ...

The distance between two skew lines with equations x = x_1+(x_2-x_1)s (1) x = x_3+(x_4-x_3)t (2) is given by D=(|(x_3-x_1)·[(x_2-x_1)x(x_4-x_3)]|)/(|(x_2-x_1)x(x_4-x_3)|) (3) ...

For a logarithmic spiral given parametrically as x = ae^(bt)cost (1) y = ae^(bt)sint, (2) evolute is given by x_e = -abe^(bt)sint (3) y_e = abe^(bt)cost. (4) As first shown ...

A path, also known as a rhumb line, which cuts a meridian on a given surface at any constant angle but a right angle. If the surface is a sphere, the loxodrome is a spherical ...

The mean tangent diameter of a solid, also known as the mean caliper diameter, is the caliper dimension obtained by averaging over all orientations.

Let five circles with concyclic centers be drawn such that each intersects its neighbors in two points, with one of these intersections lying itself on the circle of centers. ...

Ono (1914) conjectured that the inequality 27(b^2+c^2-a^2)^2(a^2+c^2-b^2)^2(a^2+b^2-c^2)^2<=(4K)^6 holds true for all triangles, where a, b, and c are the lengths of the ...