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The Euler triangle formula states that the distance d between the incenter and circumcenter of a triangle is given by d^2=R(R-2r), where R is the circumradius and r is the ...

A Taylor series remainder formula that gives after n terms of the series R_n=(f^((n+1))(x^*))/(n!p)(x-x^*)^(n+1-p)(x-x_0)^p for x^* in (x_0,x) and any p>0 (Blumenthal 1926, ...

A formula also known as the Legendre addition theorem which is derived by finding Green's functions for the spherical harmonic expansion and equating them to the generating ...

Tait's Hamiltonian graph conjecture asserted that every cubic polyhedral graph is Hamiltonian. It was proposed by Tait in 1880 and refuted by Tutte (1946) with a ...

The Tutte 8-cage (Godsil and Royle 2001, p. 59; right figure) is a cubic graph on 30 nodes and 45 edges which is the Levi graph of the Cremona-Richmond configuration. It ...

The Lagrange interpolating polynomial is the polynomial P(x) of degree <=(n-1) that passes through the n points (x_1,y_1=f(x_1)), (x_2,y_2=f(x_2)), ..., (x_n,y_n=f(x_n)), and ...

The 12-vertex graph consisting of a cube in which two opposite faces (say, top and bottom) have edges drawn across them which connect the centers of opposite sides of the ...

The cubic Archimedean graph on 24 nodes and 36 edges that is the skeleton of the truncated cube. It is implemented in the Wolfram Language as ...

The cubic Archimedean graph on 60 nodes and 90 edges that is the skeleton of the truncated dodecahedron. It is implemented in the Wolfram Language as ...

A complex map is a map f:C->C. The following table lists several common types of complex maps. map formula domain complex magnification f(z)=az a in R, a>0 complex rotation ...