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The osculating circle of a curve C at a given point P is the circle that has the same tangent as C at point P as well as the same curvature. Just as the tangent line is the ...

A ruled surface is a surface that can be swept out by moving a line in space. It therefore has a parameterization of the form x(u,v)=b(u)+vdelta(u), (1) where b is called the ...

An extension F of a field K is said to be algebraic if every element of F is algebraic over K (i.e., is the root of a nonzero polynomial with coefficients in K).

A field K is said to be algebraically closed if every polynomial with coefficients in K has a root in K.

A procedure for finding the quadratic factors for the complex conjugate roots of a polynomial P(x) with real coefficients. (1) Now write the original polynomial as ...

The free part of the homology group with a domain of coefficients in the group of integers (if this homology group is finitely generated).

The Bowley skewness, also known as quartile skewness coefficient, is defied by ((Q_3-Q_2)-(Q_2-Q_1))/(Q_3-Q_1)=(Q_1-2Q_2+Q_3)/(Q_3-Q_1), where the Qs denote the interquartile ...

Two or more lines are said to be concurrent if they intersect in a single point. Two lines concur if their trilinear coordinates satisfy |l_1 m_1 n_1; l_2 m_2 n_2; l_3 m_3 ...

The surface given by the parametric equations x = e^(bv)cosv+e^(av)cosucosv (1) y = e^(bv)sinv+e^(av)cosusinv (2) z = e^(av)sinu. (3) For a=b=1, the coefficients of the first ...

The crossed trough is the surface z=x^2y^2. (1) The coefficients of its first fundamental form are E = 1+4x^2y^4 (2) F = 4x^3y^3 (3) G = 1+4x^4y^2 (4) and of the second ...