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Let kappa_1 and kappa_2 be the principal curvatures, then their mean H=1/2(kappa_1+kappa_2) (1) is called the mean curvature. Let R_1 and R_2 be the radii corresponding to ...

The third power point is the triangle center with triangle center function alpha_(32)=a^3. It is Kimberling center X_(32).

An augmented matrix is a matrix obtained by adjoining a row or column vector, or sometimes another matrix with the same vertical dimension. The most common use of an ...

A matrix that has undergone Gaussian elimination is said to be in row echelon form or, more properly, "reduced echelon form" or "row-reduced echelon form." Such a matrix has ...

Nonhomogeneous matrix equations of the form Ax=b (1) can be solved by taking the matrix inverse to obtain x=A^(-1)b. (2) This equation will have a nontrivial solution iff the ...

The maximum and minimum of the normal curvature kappa_1 and kappa_2 at a given point on a surface are called the principal curvatures. The principal curvatures measure the ...

A surface of constant Gaussian curvature that can be given parametrically by x = a(Ucosu-U^'sinu) (1) y = -a(Usinu+U^'cosu) (2) z = v-aV^', (3) where U = ...

The pseudosphere is the constant negative-Gaussian curvature surface of revolution generated by a tractrix about its asymptote. It is sometimes also called the tractroid, ...

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 ...

A generalization of the helicoid to the parametric equations x(u,v) = avcosu (1) y(u,v) = bvsinu (2) z(u,v) = cu. (3) In this parametrization, the surface has first ...