Read e-book online Serious fun with flexagons: a compendium and guide PDF

By L.P. Pook

ISBN-10: 9048125022

ISBN-13: 9789048125029

A flexagon is a movement constitution that has the looks of a hoop of hinged polygons. it may be flexed to demonstrate various pairs of faces, often in cyclic order. Flexagons could be preferred as toys or puzzles, as a leisure arithmetic subject, and because the topic of significant mathematical learn. plausible paper types of flexagons are effortless to make and exciting to control. the maths of flexagons is complicated, and the way a flexagon works isn't instantly seen on exam of a paper version. contemporary geometric research, incorporated within the e-book, has superior theoretical figuring out of flexagons, particularly relationships among differing types.

This profusely illustrated publication is prepared in a logical order acceptable for a textbook at the geometry of flexagons. it truly is written in order that it may be loved at either the leisure arithmetic point, and on the critical arithmetic point. the one prerequisite is a few wisdom of uncomplicated geometry, together with homes of polygons. A function of the e-book is a compendium of over a hundred nets for making paper types of a few of the extra fascinating flexagons, selected to counterpoint the textual content. those are effectively drawn and reproduced at part complete dimension. a number of the nets haven't formerly been released. directions for assembling and manipulating the flexagons are included.

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3). Broadly, fundamental edge flexagons are the equivalent of regular polyhedra in that they are constructed from identical regular convex polygons, and have a high degree of symmetry in their structure. They also have a high degree of symmetry in their dynamic properties. Pats are, in general, fan folded piles of leaves. Alternate pats can be single leaves. Fundamental edge flexagons are solitary flexagons which means, broadly, that they are equivalent to single polyhedra. Many other types of flexagon can be regarded as modified fundamental edge flexagons, so an understanding of their structure and dynamic properties is an essential prerequisite to the understanding of flexagons in general.

Even edge rings of silver triangles and bronze triangles are illustrated in the next section. Further illustrations of edge rings of irregular polygons are included in Chapter 10. 1), and are as follows. 3). 9) between each pair of adjacent polygons. Regular even edge rings of identical irregular convex polygons are always possible. A slant or flat regular even edge ring consisting of 2n irregular polygons can have either 2n-fold or n-fold rotational symmetry, about an axis perpendicular to the ring, depending on both the type of polygon and type of ring.

8 A flexagon as a skew regular odd edge ring of five squares 20 2 Polygon Rings A composite number is a number that has factors other than 1 and itself. If the number of regular convex polygons in a skew regular odd edge ring is a composite number, then the ring can be arranged with a rotational symmetry that is a factor of the number. For example, a skew regular odd edge ring of nine regular polygons can be arranged with threefold rotational symmetry. Skew regular odd edge rings of regular polygons cannot be flattened if the number of polygons in the ring is a prime number.

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Serious fun with flexagons: a compendium and guide by L.P. Pook

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