Serious Fun with Flexagons

This profusely illustrated book on the geometry of flexagons is written to accommodate both recreational and serious mathematical study. It includes recent geometric analysis and over 700 nets and instructions for making paper models of various flexagons.

A flexagon is a motion structure that has the appearance of a ring of hinged polygons. It can be flexed to display different pairs of faces, usually in cyclic order. Flexagons can be appreciated as toys or puzzles, as a recreational mathematics topic, and as the subject of serious mathematical study. Workable paper models of flexagons are easy to make and entertaining to manipulate. The mathematics of flexagons is complex, and how a flexagon works is not immediately obvious on examination of a paper model. Recent geometric analysis, included in the book, has improved theoretical understanding of flexagons, especially relationships between different types.

This profusely illustrated book is arranged in a logical order appropriate for a textbook on the geometry of flexagons. It is written so that it can be enjoyed at both the recreational mathematics level, and at the serious mathematics level. The only prerequisite is some knowledge of elementary geometry, including properties of polygons. A feature of the book is a compendium of over 100 nets for making paper models of some of the more interesting flexagons, chosen to complement the text. These are accurately drawn and reproduced at half full size. Many of the nets have not previously been published. Instructions for assembling and manipulating the flexagons are included.

Further analysis has led to a much better understanding of the dynamic behaviour of flexagons, from a serious mathematics viewpoint Includes extensive information on the mathematical background to various types of flexagons and their relationships to each other A geometric approach is used throughout, and the book is profusely illustrated Geometric and aesthetic aspects of flexagons can only be fully appreciated by manipulating paper models. Nets and assembly instructions for numerous flexagons are therefore included Includes supplementary material: sn.pub/extras

Auteur

Since my formal retirement in 1998 I have been a Visiting Professor in the Department of Mechanical Engineering at University College London, where I do some part time teaching in the fields of metal fatigue and fracture mechanics. I am a senior official of the European Structural Integrity Society, and have been involved with the organisation of two of their conferences (FCP 2003 and CP 2006), including editing conference proceedings and associated special issues of journals.

Contenu
Polygon Rings.- Fundamental Nets.- Fundamental Edge Flexagons.- Fundamental Skeletal and Point Flexagons.- Fundamental Compound Edge Flexagons.- Irregular Cycle Flexagons.- Degenerate Flexagons.- Irregular Ring Even Edge Flexagons.- Irregular Polygon Edge Flexagons.- Complex Flexagons.- Miscellaneous Flexagons.