Скачать или смотреть GPW 2025 - Martin Becker - Recreational Math: Of Planes, Perfect Differences and Pretzel Graphs

Some math questions are easy enough to understand without any background in advanced mathematics that they may entertain amateurs and professionals alike. This does not mean answers will be just as easy, only that a wider audience may be able to appreciate them, and even venture one or another contribution. Welcome to recreational math.

This episode takes a look at some aspects of planes and planarity, or lack thereof, with applications in graph theory and design theory, and behind the scenes of a free but immensely expensively obtained CPAN module, spawned from an idea to solve a simple puzzle.

Some of us will recall (Euclidean) plane geometry from their school days, but there are quite different ways to look at planes. Out of these, we choose topology and projective geometry. If planar graphs are those you can draw without intersecting lines on a plane, what then can you draw on a pretzel?

Then again, seeking intersections rather than avoiding them takes us to projective planes. A 100-year-old construction of James Singer yielding planes of a certain kind is still related to many open questions. Can the CPAN module Math::DifferenceSet::Planar answer some? Was collecting accompanying data, taking years of CPU time, worth the effort? Relax, and judge yourself.

Präsentation: https://vera.in-ulm.de/rec-math/