Gems of Geometry - download pdf or read online

By John Barnes

ISBN-10: 3642050913

ISBN-13: 9783642050916

In response to a sequence of lectures for grownup scholars, this energetic and interesting ebook proves that, faraway from being a dusty, uninteresting topic, geometry is in reality filled with attractiveness and fascination. The author's infectious enthusiasm is positioned to take advantage of in explaining the various key thoughts within the box, beginning with the Golden quantity and taking the reader on a geometric trip through Shapes and Solids, during the Fourth size, completing with Einstein's Theories of Relativity.

Equally compatible as a present for a teen or as a nostalgic trip again into the area of arithmetic for older readers, John Barnes' publication is the precise antidote for an individual whose maths classes in school are a resource of painful thoughts. the place as soon as geometry was once a resource of bewilderment and frustration, Barnes brings enlightenment and leisure.

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2 Shapes and Solids Object Symbol Tetrahedron Cube Octahedron Dodecahedron Icosahedron {3, {4, {3, {5, {3, 3} 3} 4} 3} 5} Faces 4 6 8 12 20 Edges 6 12 12 30 30 Vertices F+V–E 4 8 6 20 12 2 2 2 2 2 39 Dihedral 70° 90° 109° 116° 138° 32' 28' 34' 11' Two other rather amazing compounds consist of five interlocking tetrahedra and five interlocking cubes. These exist because of a perhaps surprising relationship between the dodecahedron and the cube. In order to see this, first consider the effect of joining together four vertices in adjacent faces of a dodecahedron as shown in the first diagram below.

Since the belt has six rhombi it follows that the dihedral angle is 120°, the same as the angle between the sides of a hexagon. In the case of the triacontahedron there are five belts of ten rhombi from which it follows that the dihedral angle of the triacontahedron is 144°. Note that the rhombic faces of the dodecahedron and triacontahedron do not have the same shape. The ratio of the diagonals in the case of the dodecahedron is √2 whereas for the triacontahedron it is τ, the golden number. Non-convex polyhedra met the four Kepler-Poinsot regular polyhedra which have pentagrams as faces or vertex figures.

There are five such equatorial decagons and each contains one of the five sides of every pentagonal face. Incidentally, the truncated icosahedron with its 12 pentagonal faces and 20 hexagonal faces is the shape of the modern soccer ball. Of deeper interest is perhaps the recent discovery of the strange molecule of carbon, C60, whose 60 atoms are arranged as the 60 vertices of the truncated icosahedron. This allotrope of carbon is sometimes known as Buckminsterfullerene after the architect. 6} 48 Gems of Geometry figures.

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Gems of Geometry by John Barnes


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