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The curvature of a surface satisfies kappa=kappa_1cos^2theta+kappa_2sin^2theta, where kappa is the normal curvature in a direction making an angle theta with the first ...

The Euler infinity point is the intersection of the Euler line and line at infinity. Since it lies on the line at infinity, it is a point at infinity. It has triangle center ...

Define the Euler measure of a polyhedral set as the Euler integral of its indicator function. It is easy to show by induction that the Euler measure of a closed bounded ...

Legendre and Whittaker and Watson's (1990) term for the beta integral int_0^1x^p(1-x)^qdx, whose solution is the beta function B(p+1,q+1).

For R[n]>-1 and R[z]>0, Pi(z,n) = n^zint_0^1(1-x)^nx^(z-1)dx (1) = (n!)/((z)_(n+1))n^z (2) = B(z,n+1), (3) where (z)_n is the Pochhammer symbol and B(p,q) is the beta ...

The general displacement of a rigid body (or coordinate frame) with one point fixed is a rotation about some axis. Furthermore, a rotation may be described in any basis using ...

For signed distances on a line segment, AB^_·CD^_+AC^_·DB^_+AD^_·BC^_=0, since (b-a)(d-c)+(c-a)(b-d)+(d-a)(c-b)=0.

The intersection Ev of the Gergonne line and the Euler line. It has triangle center function alpha=(b(a-b+c)cosB+c(a+b-c)cosC-2a^2cosA)/(2a) and is Kimberling center X_(1375).

An event is a certain subset of a probability space. Events are therefore collections of outcomes on which probabilities have been assigned. Events are sometimes assumed to ...

10^(18) bytes. Unfortunately, the term is sometimes also used to mean 2^(60)=1024^6 bytes. However, the latter usage is deprecated, and the term exbibyte is preferred for ...