Submitted by IMAGINARY on
Ptolemy’s theorem is a classical result from ancient Greek mathematics, concerning the lengths of sides and diagonals of a polygon drawn in a circle. In this snapshot, I will explain why this theorem is still important today through its role in Teichmüller theory, a subject which seeks to describe all possible “shapes” of a surface with boundary.
Submitted by IMAGINARY on
We introduce Tadao Oda’s famous question on lattice polytopes which was originally posed at Oberwolfach in 1997 and, although simple to state, has remained unanswered. The question is motivated by a discussion of the two-dimensional case – including a proof of Pick’s Theorem, which elegantly relates the area of a lattice polygon to the number of lattice points it contains in its interior and on its boundary.
Submitted by IMAGINARY on
We describe some of the beautiful mathematical structures that arise from the study of the associativity equation. Our journey takes us from combinatorics to abstract algebra, with brief excursions through geometry and topology along the way.
Submitted by IMAGINARY on
This snapshot introduces the theory of trisections of smooth 4-manifolds, an area of exploration in low-dimensional topology aiming to make four-dimensional spaces more understandable. Along the way, we discuss the concepts of topology, dimension, manifolds, and more!
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.
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.
Submitted by IMAGINARY on
Convex polytopes are geometric objects that look deceptively simple. They occur everywhere in mathematics and have practical applications in everyday life – like organizing your grocery shopping list. In this snapshot, you get into contact with a long-standing, unsolved question in mathematics, which you can explore interactively.
Submitted by IMAGINARY on
Deciding which mall, hospital or school is closest to us is a problem we face everyday. It even comes on holidays with us, when we optimize our plans to make sure that we have enough time to visit all the attractions we want to see. In this article, we show how concepts from metric algebraic geometry help us to rise to this task while planning a weekend trip to the Black Forest.
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.
Submitted by IMAGINARY on
The wave equation in Euclidean spaces describes many natural phenomena such as sound, light, or water waves. We explore how its solutions are related to the geometric problem of how long thin cylinders can intersect each other and discuss a related open problem.