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Journal ArticleDOI

Can You Do It with Heptagons

01 Mar 1995-The Mathematical Gazette (Cambridge University Press (CUP))-Vol. 79, Iss: 484, pp 17
About: This article is published in The Mathematical Gazette.The article was published on 1995-03-01. It has received 15 citations till now.
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Journal ArticleDOI
TL;DR: Two proofs concerning 'Octagon loops' are given in this article, where the authors present a brief description of the 'rules' of the "Octagon Loops' investigation.
Abstract: 85.03 Two proofs concerning 'Octagon loops' I must admit that I had never heard of the mathematical investigation 'Octagon loops'* when I arrived in deepest Ilford to take up my first teaching post. I first encountered it during a departmental meeting at which investigative material for year nine groups was being issued, and it immediately fascinated me. I am sure that not all readers will be familiar with it, so here is a brief description of the 'rules':

14 citations

Book
15 Sep 2003
TL;DR: Flexagons are hinged polygons that have the intriguing property of displaying different pairs of faces when they are flexed as discussed by the authors, and they are easy to make and entertaining to manipulate.
Abstract: Flexagons are hinged polygons that have the intriguing property of displaying different pairs of faces when they are flexed. Workable paper models of flexagons are easy to make and entertaining to manipulate. Flexagons have a surprisingly complex mathematical structure and just how a flexagon works is not obvious on casual examination of a paper model. Flexagons may be appreciated at three different levels. Firstly as toys or puzzles, secondly as a recreational mathematics topic and finally as the subject of serious mathematical study. This book is written for anyone interested in puzzles or recreational maths. No previous knowledge of flexagons is assumed, and the only pre-requisite is some knowledge of elementary geometry. An attractive feature of the book is a collection of nets, with assembly instructions, for a wide range of paper models of flexagons. These are printed full size and laid out so they can be photocopied.

9 citations

Journal ArticleDOI
TL;DR: Loops of Regular Polygons as discussed by the authors is a variant of regular polygonal regular polygons with loops of regular regular polygons (LoOPs) and regular polygraphs.
Abstract: (2000) Loops of Regular Polygons The American Mathematical Monthly: Vol 107, No 6, pp 500-510

1 citations

Book ChapterDOI
01 Jan 2003
References
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Book
01 Jan 1969
TL;DR: In this paper, the authors describe the topology of surfaces in the Euclidean plane, including the Golden Section and Phyllotaxis, as well as the five Platonic solids.
Abstract: Triangles. Regular Polygons. Isometry in the Euclidean Plane. Two--Dimensional Crystallography. Similarity in the Euclidean Plane. Circles and Spheres. Isometry and Similarity in Euclidean Space. Coordinates. Complex Numbers. The Five Platonic Solids. The Golden Section and Phyllotaxis. Ordered Geometry. Affine Geometry. Projective Geometry. Absolute Geometry. Hyperbolic Geometry. Differential Geometry of Curves. The Tensor Notation. Differential Geometry of Surfaces. Geodesics. Topology of Surfaces. Four--Dimensional Geometry. Tables. References. Answers to Exercises. Index.

1,411 citations