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The use of coordinates (such as Cartesian coordinates) in the study of geometry. Cartesian geometry is named after René Descartes (Bell 1986, p. 48), although Descartes may ...

The number of coincidences of a (nu,nu^') correspondence of value gamma on a curve of curve genus p is given by nu+nu^'+2pgamma.

If a one-parameter family of curves has index N and class M, the number tangent to a curve of order n_1 and class m_1 in general position is m_1N+n_1M.

The dimension of a special series can never exceed half its order.

One of the Plücker characteristics, defined by p=1/2(n-1)(n-2)-(delta+kappa)=1/2(m-1)(m-2)-(tau+iota), where m is the class, n the order, delta the number of nodes, kappa the ...

An equilateral triangle is a triangle with all three sides of equal length a, corresponding to what could also be known as a "regular" triangle. An equilateral triangle is ...

Given two univariate polynomials of the same order whose first p coefficients (but not the first p-1) are 0 where the coefficients of the second approach the corresponding ...

A product of a reflection in a line and translation along the same line.

If two groups are residual to a third, every group residual to one is residual to the other. The Gambier extension of this theorem states that if two groups are ...

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.