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For a semicubical parabola with parametric equations x = t^2 (1) y = at^3, (2) the involute is given by x_i = (t^2)/3-8/(27a^2) (3) y_i = -(4t)/(9a), (4) which is half a ...

A surface given by the parametric equations x(u,v) = u (1) y(u,v) = v (2) z(u,v) = 1/3u^3-1/2v^2. (3) The coefficients of the coefficients of the first fundamental form are E ...

A space curve consisting of a spiral wound around a helix. It has parametric equations x = [R+acos(omegat)]cost (1) y = [R+acos(omegat)]sint (2) z = ht+asin(omegat). (3)

A surface generated by the parametric equations x(u,v) = ucosv (1) y(u,v) = usinv (2) z(u,v) = vcosu. (3) The above image uses u in [-4,4] and v in [0,6.25]. The coefficients ...

A Steinmetz curve is a curve of intersection of two perpendicularly placed cylinders of radii a and b comprising a Steinmetz solid. If the vertical cylinder has radius a and ...

A surface given by the parametric equations x = A(u-a)^m(v-a)^n (1) y = B(u-b)^m(v-b)^n (2) z = C(u-c)^m(v-c)^n. (3)

The evolute of the tractrix given by parametric equations x = t-tanht (1) y = secht (2) is the catenary x_e = t (3) y_e = cosht. (4)

The tractrix spiral is a spiral with parametric equations x(t) = acostcos(t-tant) (1) y(t) = acostsin(t-tant) (2) for t in [0,pi/2). It is also known as the polar tractrix or ...

A smooth two-dimensional surface given by embedding the projective plane into projective 5-space by the homogeneous parametric equations v(x,y,z)=(x^2,y^2,z^2,xy,xz,yz). The ...

The right conoid surface given by the parametric equations x(u,v) = vcosu (1) y(u,v) = vsinu (2) z(u,v) = csqrt(a^2-b^2cos^2u). (3)