information:highlighting, structural:summarization, structural:scholar_edition
Lemniscate of Gerono

Another lemniscate, the lemniscate of Gerono or lemniscate of Huygens, is the zero set of the quartic polynomial y 2 − x 2 (a 2 − x 2) {\displaystyle y^{2}-x^{2}(a^{2}-x^{2})}. Viviani's curve, a three-dimensional curve formed by intersecting a sphere with a cylinder, also has a figure eight shape, and has the lemniscate of Gerono as its planar projection.