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This delightful geometric property was familiar to French secondary-school students in the 1970s, although few knew how to prove it.
By the end of the 19th century, following the work of Poincaré and many other mathematicians, including Bernhard Riemann (1826–1866) and Enrico Betti (1823–1892), the topology of surfaces in our ordinary space was well understood.
Roulettes do not exhaust the possibilities offered by plane-on-plane motion—or the geometric wonders hidden within it. Armed once again with drawing paper, tracing paper and pens, we continue our exploration with some somewhat overlooked curves: glissettes.
It is easy to overlook, but many geometric problems can be solved by iterative methods or, more broadly, algorithms. These questions are the subject of computational geometry! This is a vibrant, highly active field in which many seemingly elementary questions still await solutions.
