Download Gems of Geometry by John Barnes PDF

By John Barnes

In keeping with a sequence of lectures for grownup scholars, this full of life and interesting ebook proves that, faraway from being a dusty, boring topic, geometry is in truth jam-packed with good looks and fascination. The author's infectious enthusiasm is placed to take advantage of in explaining a number of the key suggestions within the box, beginning with the Golden quantity and taking the reader on a geometric trip through Shapes and Solids, throughout the Fourth measurement, completing with Einstein's Theories of Relativity.

Equally compatible as a present for an adolescent or as a nostalgic trip again into the realm of arithmetic for older readers, John Barnes' publication is the correct antidote for someone whose maths classes in school are a resource of painful thoughts. the place as soon as geometry used to be a resource of bewilderment and frustration, Barnes brings enlightenment and leisure.

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In this case there are six intersecting equatorial decagons and these can be joined by 20 triangles or by 12 pentagons. 4} as shown overleaf. This does not have equatorial polygons but instead has pairs of octagons on either side of the equatorial belts of squares and so positioned a bit like the arctic and antarctic circles of the earth. Moreover, there are three such belts of squares intersecting at right angles. So we start with six octagons in three parallel pairs intersecting each other at right angles.

The remaining six can be introduced in various ways but a good way is to consider some of the remaining tilings and what happens if we reduce the number of polygons around a key polygon. 12} shown below left which has alternate hexagons and squares arranged around a dodecagon. 10} which is sometimes called the truncated icosidodecahedron. 8} the truncated cuboctahedron. 4} which is that formed by overlapping dodecagons. More explicitly, it consists of squares and triangles around a hexagon. 4} which is known as the rhombicosidodecahedron for reasons which need not bother us.

A first step in its understanding can be obtained by considering the face of one cube (the white one for example) and the lines of intersection of the four other cubes with it. This is shown opposite where the intersecting cubes are coloured red, blue, green and yellow and the intersecting lines have the appropriate colour. Note that the cubes intersect each other in triangles so that the figure is just four overlapping triangles; the common area is a rhombus which will be mentioned again later.

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