In the 19th century, mathematicians became interested in the question how mathematical functions look like. Felix Klein, a German mathematician, had several of such physical models in his lab in Göttingen, and popularized them in America when he brought a boatload to the World's Fair in Chicago in 1893. The photo above shows a model of a Clebsch surface from 1880, designed and presumably built by Adolf Weiler, Klein's grad student. It is kept today at the University of Göttingen. Sources: Joshua Batson, This Is What Math Equations Look Like in 3-D, Wired (2014) Göttingen University Clebsch's diagonal surface (thanks to Alba Marina Málaga Sabogal for sending us this reference).

These cams are solid models of bivariate and univariate mathematical functions plotted in cylindric coordinates (left and middle images) and polar coordinates (right image). They were not meant to be visually examined, but were used in mechanical analog computers for aiming battleship guns during WWII. They were also called computing cams. Mechanical fire control aids started to be developed in the 1900s and and were still in use in the late 1980s. During WWII, they could solve multivariate calculus problems in real-time. While cams were used for hard-coded functions, gears were used for arithmetic calculations and other specialized devices were used for multiplication and differential calculus. The design of these analog computers is clearly explained in the video and PDFs linked below. The oldest known mechanical analog computer is from 150BC (see our entry greek orrery). Cams were already used in 300BC to control automata, and were further developed in the 13th century by polymath Ismail al-Jazari. Sources: US Navy (1953) Basic Mechanisms in Fire Control Computers (Video). US Navy (1944) Basic Fire Control Mechanisms (PDF files). Sean Gallagher (2014) Gears of war: When mechanical analog computers ruled the waves. Wikipedia articles on Rangekeepers, Cams, and al-Jazari.