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A ternary diagram is a triangular diagram which displays the proportion of three variables that sum to a constant and which does so using barycentric coordinates. The ...

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three ...

Given a reference triangle DeltaABC, the trilinear coordinates of a point P with respect to DeltaABC are an ordered triple of numbers, each of which is proportional to the ...

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy ...

The smallest number of times u(K) a knot K must be passed through itself to untie it. Lower bounds can be computed using relatively straightforward techniques, but it is in ...

Probability and Statistics

A circle packing is an arrangement of circles inside a given boundary such that no two overlap and some (or all) of them are mutually tangent. The generalization to spheres ...

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...

In general, the external similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...

The base 2 method of counting in which only the digits 0 and 1 are used. In this base, the number 1011 equals 1·2^0+1·2^1+0·2^2+1·2^3=11. This base is used in computers, ...