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A generalization of Poncelet's continuity principle made by H. Schubert in 1874-1879. The conservation of number principle asserts that the number of solutions of any ...

Schubert's application of the conservation of number principle.

An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity. The understanding of infinitesimals was a major ...

One of the numbers ..., -2, -1, 0, 1, 2, .... The set of integers forms a ring that is denoted Z. A given integer n may be negative (n in Z^-), nonnegative (n in Z^*), zero ...

Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...

A direct search method of optimization that works moderately well for stochastic problems. It is based on evaluating a function at the vertices of a simplex, then iteratively ...

An elliptic curve is the set of solutions to an equation of the form y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6. (1) By changing variables, y->2y+a_1x+a_3, assuming the field ...

A "curve" (i.e., a continuous map of a one-dimensional interval) into a two-dimensional area (a plane-filling function) or a three-dimensional volume.

An acnode, also called an isolated point or hermit point, of a curve is a point that satisfies the equation of the curve but has no neighboring points that also lie on the ...

A quartic curve that resembles the symbol for the zodiacal sign Capricorn given by the implicit equation a^2x^2(x^2+y^2)-b(ay-x^2-y^2)^2=0, where a>0, b>a^2. The curve ...