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The angle obtained by drawing the auxiliary circle of an ellipse with center O and focus F, and drawing a line perpendicular to the semimajor axis and intersecting it at A. ...

G_(ab)=R_(ab)-1/2Rg_(ab), where R_(ab) is the Ricci curvature tensor, R is the scalar curvature, and g_(ab) is the metric tensor. (Wald 1984, pp. 40-41). It satisfies ...

A surface S is n-embeddable if it can be placed in R^n-space without self-intersections, but cannot be similarly placed in any R^k for k<n. A surface so embedded is said to ...

Endraß surfaces are a pair of octic surfaces which have 168 ordinary double points. This is the maximum number known to exist for an octic surface, although the rigorous ...

The Enneper surfaces are a three-parameter family of surfaces with constant negative curvature (and nonconstant mean curvature). In general, they are described by elliptic ...

The envelope of a one-parameter family of curves given implicitly by U(x,y,c)=0, (1) or in parametric form by (f(t,c),g(t,c)), is a curve that touches every member of the ...

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 ...

An exterior angle beta of a polygon is the angle formed externally between two adjacent sides. It is therefore equal to 2pi-alpha, where alpha is the corresponding internal ...

The term folium means "leaf" in Latin and refers and refers to a plane curve having "leaf-shaped" rounded lobes. There are a number of different sorts of folia, including ...

When referring to a planar object, "free" means that the object is regarded as capable of being picked up out of the plane and flipped over. As a result, mirror images are ...