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Four circles c_1, c_2, c_3, and c_4 are tangent to a fifth circle or a straight line iff T_(12)T_(34)+/-T_(13)T_(42)+/-T_(14)T_(23)=0. (1) where T_(ij) is the length of a ...

The symbol ∡ABC denotes the directed angle from AB to BC, which is the signed angle through which AB must be rotated about B to coincide with BC. Four points ABCD lie on a ...

The closed plane curve that crosses itself once and consists of one lobe on each side of the intersection. It can be viewed as a circle with a half twist. The fundamental ...

The great sphere on the surface of a hypersphere is the three-dimensional analog of the great circle on the surface of a sphere. Let 2h be the number of reflecting spheres, ...

A quadratic surface given by the equation x^2+2rz=0.

Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

"The" trifolium is the three-lobed folium with b=a, i.e., the 3-petalled rose curve. It is also known as the paquerette de mélibée (Apéry 1987, p. 85), with paquerette being ...

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

Consider a power series in a complex variable z g(z)=sum_(n=0)^inftya_nz^n (1) that is convergent within the open disk D:|z|<R. Convergence is limited to within D by the ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...