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The smallest radial distance of an ellipse as measured from a focus. Taking v=0 in the equation of an ellipse r=(a(1-e^2))/(1+ecosv) gives the periapsis distance r_-=a(1-e). ...

To translate an object means to perform a translation. A translate of a mathematical object means a shifted (i.e., translated) version of the object. Hence, one can speak of ...

There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...

A mathematical object S is said to be additively closed if a,b in S implies that a+b in S.

A mathematical object S is said to be multiplicatively closed if a,b in S implies that ab in S.

The isogonal transform of a geometric object is the object obtained by collectively taking the isogonal conjugates of all its points.

The isotomic transform of a geometric object is the object obtained by collectively taking the isotomic conjugates of all its points.

The north pole is the point on a sphere with maximum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

A mathematical property P holds locally if P is true near every point. In many different areas of mathematics, this notion is very useful. For instance, the sphere, and more ...

The slicing of a three-dimensional object by a plane (or more general slice).