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A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...

Given a curve C and O=(x_0,y_0) a fixed point called the pedal point, then for a point P on C, draw a line perpendicular to OP. The envelope of these lines as P describes the ...

The geodesic on an oblate spheroid can be computed analytically, although the resulting expression is much more unwieldy than for a simple sphere. A spheroid with equatorial ...

A system of equation types obtained by generalizing the differential equation for the normal distribution (dy)/(dx)=(y(m-x))/a, (1) which has solution y=Ce^((2m-x)x/(2a)), ...

An impossible figure in which a stairway in the shape of a square appears to circulate indefinitely while still possessing normal steps (Penrose and Penrose 1958). The Dutch ...

There are at least 15 classes of convex pentagonal tilings, as illustrated above. The first five were discovered during investigations of German mathematician Karl Reinhardt ...

The problem in calculus of variations to find the minimal surface of a boundary with specified constraints (usually having no singularities on the surface). In general, there ...

A point is a 0-dimensional mathematical object which can be specified in n-dimensional space using an n-tuple (x_1, x_2, ..., x_n) consisting of n coordinates. In dimensions ...

An algebraic surface of surface order 4. Unlike cubic surfaces, quartic surfaces have not been fully classified. Examples of quartic surfaces include the apple surface, ...

Let G be a finite, connected, undirected graph with graph diameter d(G) and graph distance d(u,v) between vertices u and v. A radio labeling of a graph G is labeling using ...