Viviani’s curve

The line where a sphere meets a cylinder half its width, set so that the cylinder passes through the sphere’s centre. In 1692 Viviani showed how to cut two windows of this shape from a hemisphere so that what remained could be squared with ruler and compass. Its shadows on the three coordinate planes are a circle, an arc of a parabola and a lemniscate of Gerono.

(a(1 + cos t), a sin t, 2a sin(t/2)), -2π < t < 2π

On mathcurve.com as Courbe de Viviani