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A line of constant longitude on a spheroid (or sphere). More generally, a meridian of a surface of revolution is the intersection of the surface with a plane containing the ...

The n-roll mill curve is given by the equation x^n-(n; 2)x^(n-2)y^2+(n; 4)x^(n-4)y^4-...=a^n, where (n; k) is a binomial coefficient.

An ordinary double point of a plane curve is point where a curve intersects itself such that two branches of the curve have distinct tangent lines. Ordinary double points of ...

A projective plane, sometimes called a twisted sphere (Henle 1994, p. 110), is a surface without boundary derived from a usual plane by addition of a line at infinity. Just ...

A surface constructed by placing a family of figure-eight curves into R^3 such that the first and last curves reduce to points. The surface has parametric equations x(u,v) = ...

The space of currents arising from rectifiable sets by integrating a differential form is called the space of two-dimensional rectifiable currents. For C a closed bounded ...

Find an analytic parameterization of the compact Riemann surfaces in a fixed homeomorphism class. The Ahlfors-Bers theorem proved that Riemann's moduli space gives the ...

Riemann's moduli space R_p is the space of analytic equivalence classes of Riemann surfaces of fixed genus p.

The curve b(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u) is called the directrix (or base curve).

If J is a simple closed curve in R^2, the closure of one of the components of R^2-J is homeomorphic with the unit 2-ball. This theorem may be proved using the Riemann mapping ...