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The Roman surface, also called the Steiner surface (not to be confused with the class of Steiner surfaces of which the Roman surface is a particular case), is a quartic ...

If two projective pencils of curves of orders n and n^' have no common curve, the locus of the intersections of corresponding curves of the two is a curve of order n+n^' ...

Let K be a number field and let O be an order in K. Then the set of equivalence classes of invertible fractional ideals of O forms a multiplicative Abelian group called the ...

The Jacobi elliptic functions are standard forms of elliptic functions. The three basic functions are denoted cn(u,k), dn(u,k), and sn(u,k), where k is known as the elliptic ...

An algebraic surface of order 3. Schläfli and Cayley classified the singular cubic surfaces. On the general cubic, there exists a curious geometrical structure called double ...

In Note M, Burnside (1955) states, "The contrast that these results shew between groups of odd and of even order suggests inevitably that simple groups of odd order do not ...

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 ...

The surface with parametric equations x = (sinhvcos(tauu))/(1+coshucoshv) (1) y = (sinhvsin(tauu))/(1+coshucoshv) (2) z = (coshvsinh(u))/(1+coshucoshv), (3) where tau is the ...

A Monge patch is a patch x:U->R^3 of the form x(u,v)=(u,v,h(u,v)), (1) where U is an open set in R^2 and h:U->R is a differentiable function. The coefficients of the first ...

Neville's algorithm is an interpolation algorithm which proceeds by first fitting a polynomial of degree 0 through the point (x_k,y_k) for k=1, ..., n, i.e., P_k(x)=y_k. A ...