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The five Platonic solids and their connection to root systems

Submitted by IMAGINARY on

Platonic solids have fascinated humans for thousands of years. In ancient times, they were associated with the elements fire, air, water, earth, and aether. These solids are completely symmetrical three-dimensional polyhedra. In this snapshot, it is first explained that there can only be five such polyhedra in the threedimensional space. For this purpose, so-called Schläfli symbols and Coxeter graphs are introduced. More precisely, the (linear) Coxeter graphs correspond to the (linear) Schläfli symbols that, in turn, correspond exactly to the regular convex polyhedra.

Five ways to spell ADE

Submitted by IMAGINARY on

The solutions to a surprising number of mathematical questions can be classified by the ADE Coxeter–Dynkin diagrams. This snapshot will show you a selection of these questions and how they correspond to the ADE Coxeter–Dynkin diagrams.

Hilbert marble run

Submitted by Paul REMY on

Here is a marble run inspired by the famously known Hilbert space filling curves, with this you are able to 3d print lego compatible marble run of any size.

There are 6 different models necessary to build every iteration wanted; each of them is based on the 2nd iteration of the Hilbert curves.

Exhibition catalog "Pracht en kracht van wiskunde"

Submitted by IMAGINARY on

The Dutch catalog for the exhibition “Pracht en kracht van wiskunde,” which toured Belgium and the Netherlands in 2022 and 2023, is available here.

This gallery contains additional information about the exhibition, posters in English and Dutch, and other materials.

The geometry of fair division

Submitted by IMAGINARY on

How can we fairly divide a necklace with various types of beads? We use this problem as a motivating example to explain how geometry naturally appears in solutions of non-geometric problems. The strategy we develop to solve this problem has been used in several other contexts.

Patterns and waves in theory, experiment, and application

Submitted by IMAGINARY on

In this snapshot of modern mathematics we describe some of the most prevalent waves and patterns that can arise in mathematical models and which are used to describe a number of biological, chemical, physical, and social processes. We begin by focussing on two types of patterns that do not change in time: space-filling patterns and localized patterns.

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