Bulge Head: a strangely round volume.

thingiverse

The model depicts the volume above the xy-plane, outside a unit sphere, and inside the cardioid of revolution defined by Rho=1+Cos(Phi) in spherical coordinates. A classic problem in Multivariable Calculus asks for the volume of this solid, with using spherical coordinates being the most straightforward approach. Alternatively, consider the region in the xy-plane above the y-axis, outside the unit circle, and inside the cardioid r=1+Cos(Theta) in polar coordinates. When this region is revolved around the y-axis, it creates a volume of revolution known as the "bulge head" solid. This object was created and 3D printed by Ryan McDonnell, a summer research student at WLU in '17. For more information about this model, visit http://mathvis.academic.wlu.edu/2015/07/21/bulge-head-solid/.