2018 – Solving the Shortest Route Problem with a 3D Printer

Christian Freksa, a professor of Cognitive Systems at the Department of Informatics at the University of Bremen, shows how a shortest route can be computed by 3D-printing the route network using flexible material, and then pulling apart the start and end nodes. The tight portion of the network immediately gives the shortest route. The right image shows an earlier version using strings.

This idea was first proposed by mathematician George Minty in 1957, in a short letter to the editor of the Operations Research journal. It was later popularized by Alexander Dewdney. 

Sources:

1. Christian Freksa, Thomas Barkowsky, Zoe Falomir and Jasper van de Ven (2018) Geometric Problem Solving with Strings and Pins. To appear in Spatial Cognition and Computation.
2. Christian Freksa (2015) Strong Spatial Cognition.
3. George G. Minty (1957) A Comment on the Shortest-Route Problem.
4. First and second image from the 2018 article, last image from the 2015 article.