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A line of constant longitude on a spheroid (or sphere). More generally, a meridian of a surface of revolution is the intersection of the surface with a plane containing the ...

Let f and g be nonnegative and continuous functions on the closed interval [a,b], then the solid of revolution obtained by rotating the curves f(x) and g(x) about the x-axis ...

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 ...

Pathological functions that are continuous but differentiable only on a set of points of measure zero are sometimes known as monsters of real analysis. Examples include the ...

A nonuniform rational B-spline curve defined by C(t)=(sum_(i=0)^(n)N_(i,p)(t)w_iP_i)/(sum_(i=0)^(n)N_(i,p)(t)w_i), where p is the order, N_(i,p) are the B-spline basis ...

Let gamma be a path in C, w=f(z), and theta and phi be the tangents to the curves gamma and f(gamma) at z_0 and w_0. If there is an N such that f^((N))(z_0) != 0 (1) ...

A ruled surface parameterization x(u,v)=b(u)+vg(u) is called noncylindrical if gxg^' is nowhere 0. A noncylindrical ruled surface always has a parameterization of the form ...

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 ...

Let M subset R^3 be a regular surface and u_(p) a unit tangent vector to M, and let Pi(u_(p),N(p)) be the plane determined by u_(p) and the normal to the surface N(p). Then ...

Any continuous cumulative frequency curve, such as the one illustrated above in the right figure.