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A surface of revolution defined by Kepler. It consists of more than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

In affine three-space the Cayley surface is given by x_3=x_1x_2-1/3x_1^3 (1) (Nomizu and Sasaki 1994). The surface has been generalized by Eastwood and Ezhov (2000) to ...

The corkscrew surface, sometimes also called the twisted sphere (Gray 1997, p. 477), is a surface obtained by extending a sphere along a diameter and then twisting. It can be ...

A generalization to a quartic three-dimensional surface is the quartic surface of revolution (x^4-ax^3)+a^2(y^2+z^2)=0, (1) illustrated above. With a=1, this surface is ...

A constant-curvature surface which can be given parametrically by x = rcosphi (1) y = rsinphi (2) z = (ln[tan(1/2v)]+a(C+1)cosv)/(sqrt(C)), (3) where phi = ...

A surface with boundary is a topological space obtained by identifying edges and vertices of a set of triangles according to all the requirements of a surface except that ...

A surface (or "space") of section, also called a Poincaré section (Rasband 1990, pp. 7 and 93-94), is a way of presenting a trajectory in n-dimensional phase space in an ...

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

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

The function f(x,y)=(2x^2-y)(y-x^2) which does not have a local maximum at (0, 0), despite criteria commonly touted in the second half of the 1800s which indicated the ...