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Let (xi_1,xi_2) be a locally Euclidean coordinate system. Then ds^2=dxi_1^2+dxi_2^2. (1) Now plug in dxi_1=(partialxi_1)/(partialx_1)dx_1+(partialxi_1)/(partialx_2)dx_2 (2) ...

The curve with trilinear coordinates a^t:b^t:c^t for a given power t.

Given a vector space V, its projectivization P(V), sometimes written P(V-0), is the set of equivalence classes x∼lambdax for any lambda!=0 in V-0. For example, complex ...

One of the four regions of the plane defined by the four possible combinations of signs (+,+), (+,-), (-,+), and (-,-) for (x,y).

The general bivariate quadratic curve can be written ax^2+2bxy+cy^2+2dx+2fy+g=0. (1) Define the following quantities: Delta = |a b d; b c f; d f g| (2) J = |a b; b c| (3) I = ...

A real function is said to be analytic if it possesses derivatives of all orders and agrees with its Taylor series in a neighborhood of every point.

A triangle center is regular iff there is a triangle center function which is a polynomial in Delta, a, b, and c (where Delta is the area of the triangle) such that the ...

If two algebraic plane curves with only ordinary singular points and cusps are related such that the coordinates of a point on either are rational functions of a ...

A topological space having a countable dense subset. An example is the Euclidean space R^n with the Euclidean topology, since it has the rational lattice Q^n as a countable ...

An algebraic surface of degree 7. The Labs septic is an example of a septic surface.