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If a sequence of double points is passed as a closed curve is traversed, each double point appears once in an even place and once in an odd place.

A disk D in a solid torus V=S^1×D^2 is called meridinal if its boundary is a nontrivial curve in del V (so that it is a meridian). Then a closed subset X subset V is called ...

The four-dimensional version of the gradient, encountered frequently in general relativity and special relativity, is del _mu=[1/cpartial/(partialt); partial/(partialx); ...

A general term which refers to an increase (or decrease in the case of the oxymoron "negative growth") in a given quantity.

The contour C_epsilon illustrated above.

H=|aa^'a^('')|a_(x^(n-2))a_(x^(n-2))^'a_(x^(n-2))^('')=0. The nonsingular inflections of a curve are its nonsingular intersections with the Hessian.

Let Gamma be an algebraic curve in a projective space of dimension n, and let p be the prime ideal defining Gamma, and let chi(p,m) be the number of linearly independent ...

Every modular system has a modular system basis consisting of a finite number of polynomials. Stated another way, for every order n there exists a nonsingular curve with the ...

The hippopede, also known as the horse fetter, is a curve given by the polar equation r^2=4b(a-bsin^2theta). Hippopedes are plotted above for values of a/b=0.2 to 2.0.

The configuration formed by two curves starting at a point, called the vertex V, in a common direction. Horn angles are concrete illustrations of non-Archimedean geometries.