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An archaic name for the torus.

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 ...

An algebraic surface of degree 12. Examples of dodecic surfaces include the figure-eight parametrization of the Klein bottle and Sarti dodecic.

A surface that contains two families of rulings. The only three doubly ruled surfaces are the plane, hyperbolic paraboloid, and single-sheeted hyperboloid.

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 ...

The surface of revolution generated by the external catenary between a fixed point a and its conjugate on the envelope of the catenary through the fixed point is equal in ...

A surface given by the parametric equations x(u,v) = u (1) y(u,v) = v (2) z(u,v) = au^4+u^2v-v^2. (3)

A nonuniform rational B-spline surface of degree (p,q) is defined by ...

A ruled surface M is a normal developable of a curve y if M can be parameterized by x(u,v)=y(u)+vN^^(u), where N is the normal vector (Gray 1993, pp. 352-354; first edition ...