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"Nordstrand's weird surface" is an attractive quartic surface given by the implicit equation It has 11 ordinary double points located at (2/5,0,0), (-2/5,0,0), ...

A parallel of a surface of revolution is the intersection of the surface with a plane orthogonal to the axis of revolution.

The curve b(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u) is called the directrix (or base curve).

The envelope of the plane lx+my+nz=c, (1) where c is the speed of propagation of a wave in the direction (l,m,n) (i.e., l, m, and n are the direction cosines) is known as the ...

A surface which is related to Cayley numbers.

A three-dimensional shadow of a four-dimensional Klein bottle.

An expanded paper bag, cushion, or pillow has a distinctive shape. Given the dimensions of a flat rectangular bag with dimensions a, b, bounds for the maximum volume of ...

A parameterization is isothermal if, for zeta=u+iv and phi_k(zeta)=(partialx_k)/(partialu)-i(partialx_k)/(partialv), the identity phi_1^2(zeta)+phi_2^2(zeta)+phi_3^2(zeta)=0 ...

On the surface of a sphere, attempt separation of variables in spherical coordinates by writing F(theta,phi)=Theta(theta)Phi(phi), (1) then the Helmholtz differential ...

A class of complete orientable minimal surfaces of R^3 derived from Enneper's minimal surface. They are named for the mathematicians who found the first two examples in 1982. ...