Reflections on Mathematics

Connection to other fields Image: 

Math Creations - A Math-Art Competition

We describe a math-art contest for new creative ideas and their realizations based on modern mathematical concepts currently worked on in two Berlin-based collaborative research centers. By combining mathematics with art and design the power, the fun, and the beauty of this interdisciplinary connection is shown.

The Willmore Conjecture

The Willmore problem studies which torus has the least amount of bending energy. We explain how to think of a torus as a donut-shaped surface and how the intuitive notion of bending has been studied by mathematics over time. 

Collaborative Mathematics Communication - Experiences and Examples

In this paper we discuss experiences with a collaborative and participative approach of communicating mathematics to a broad audience. We give a list of recommendations and ideas, how the public itself can be involved in creating mathematics exhibits and can become an integral part of outreach activities. The ideas are accompanied by sample activities we carried out within “IMAGINARY – open mathematics”, a project by the Mathematisches Forschungsinstitut Oberwolfach supported by the Klaus Tschira Stiftung.

Mathematikon: A Mathematical Shopping Center

We describe the permanent integration of mathematical content into a shopping center in Heidelberg, Germany. Main features are a mathematical image gallery, conveyor belt designs, a multi touch screen station, riddles in the bathroom, and at the bakery, classic quotes, as well as a temporary shop window display.

Das Problem der Kugelpackung

Wie würdest du Tennisbälle oder Orangen stapeln? Oder allgemeiner formuliert: Wie dicht lassen sich identische 3-dimensionale Objekte überschneidungsfrei anordnen? Das Problem, welches auch Anwendungen in der digitalen Kommunikation hat, hört sich einfach an, ist jedoch für Kugeln in höheren Dimensionen noch immer ungelöst. Sogar die Berechnung guter Näherungslösungen ist für die meisten Di- mensionen schwierig. 

Curriculum development in university mathematics: where mathematicians and education collide

This snapshot looks at educational aspects of the design of curricula in mathematics. In particular, we examine choices textbook authors have made when introducing the concept of the completness of the real numbers. Can significant choices really be made? Do these choices have an effect on how people learn, and, if so, can we understand what they are?

Katzengold: Pyrite, Plato, and a Polynomial

What are the similarities of the mineral pyrite, the dodecahedron as the fifth Platonic solid, and a polynomial of degree 16? This paper explores this connection by using the free software SURFER of the IMAGINARY open mathematics platform, which leads to fascinating pictures displaying transformations from a cube to a dodecahedron, to a rhombic dodecahedron, and to an octahedron, using a single formula. A survey on the ideas and the mathematics behind these visualizations is given.

How to make an IMAGINARY Exhibition - Bridges 2013 Paper

This paper presented at the BRIDGES conference 2013 provides a brief overview of the main steps needed for organizing a math art exhibition. As IMAGINARY visited more locations, we realized the need for providing some hints and advice based on the experience of former exhibitions. Our goal is to motivate you to make your own exhibition and to contribute to the IMAGINARY platform with your own exhibits.

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