Straight lines on models of curved surfaces (Q2400831)

The investigation of 3-dimensional surfaces of degree three started in the middle of the 19th century by Arthur Cayley, George Salmon, Ludwig Schläfli and Alfred Clebsch. In 1849, Salmon proved that in general cubic surfaces contain exactly 27 straight lines in projective 3-space over the complex numbers. Cayley and Schläfli studied the highly symmetric incidence properties of these lines. This development led to an interest in building physical models to better understand cubic surfaces. At the end of the 19th century, many universities had collections of such models. The author describes these developments and uses computer generated pictures and 3D-printing to study and visualize the surfaces. He shows the results and discuss the problems involved in the use of 3D-printing for this purpose.