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Let O and I be the circumcenter and incenter of a triangle with circumradius R and inradius r. Let d be the distance between O and I. Then d^2=R(R-2r) (Mackay 1886-1887; ...

An Eulerian path, also called an Euler chain, Euler trail, Euler walk, or "Eulerian" version of any of these variants, is a walk on the graph edges of a graph which uses each ...

The system of partial differential equations describing fluid flow in the absence of viscosity, given by (partialu)/(partialt)+u·del u=-(del P)/rho, where u is the fluid ...

_2F_1(a,b;c;z)=int_0^1(t^(b-1)(1-t)^(c-b-1))/((1-tz)^a)dt, (1) where _2F_1(a,b;c;z) is a hypergeometric function. The solution can be written using the Euler's ...

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 ...

The Evans conic is the conic section passing through the Fermat points X and X^', the inner and outer Napoleon points N and N^', and the isodynamic points S and S^' of a ...

A univariate function f(x) is said to be even provided that f(x)=f(-x). Geometrically, such functions are symmetric about the y-axis. Examples of even functions include 1 ...

(1) for p in [0,1], where delta is the central difference and E_(2n) = G_(2n)-G_(2n+1) (2) = B_(2n)-B_(2n+1) (3) F_(2n) = G_(2n+1) (4) = B_(2n)+B_(2n+1), (5) where G_k are ...

A curve on the unit sphere S^2 is an eversion if it has no corners or cusps (but it may be self-intersecting). These properties are guaranteed by requiring that the curve's ...

A differential of the form df=P(x,y)dx+Q(x,y)dy (1) is exact (also called a total differential) if intdf is path-independent. This will be true if ...