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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 ...

Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not explicitly derive equations for such surfaces. Beauville ...

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 ...

A surface parameterized in variables u and v is called smooth if the tangent vectors in the u and v directions satisfy T_uxT_v!=0, where AxB is a cross product.

Any linear combination of real spherical harmonics A_lP_l(costheta)+sum_(m=1)^l[A_l^mcos(mphi)+B_l^msin(mphi)]P_l^m(costheta) for l fixed whose sum is not premultiplied by a ...