Download Gems of Geometry by John Barnes PDF
By John Barnes
Based on a chain of lectures for grownup scholars, this energetic and unique ebook proves that, faraway from being a dusty, uninteresting topic, geometry is in truth packed with good looks and fascination. The author's infectious enthusiasm is positioned to exploit in explaining the various key suggestions within the box, beginning with the Golden quantity and taking the reader on a geometric trip through Shapes and Solids, in the course of the Fourth size, completing with Einstein's Theories of Relativity.
Equally compatible as a present for an adolescent or as a nostalgic trip again into the area of arithmetic for older readers, John Barnes' ebook is the precise antidote for a person whose maths classes in class are a resource of painful stories. the place as soon as geometry used to be a resource of misunderstanding and frustration, Barnes brings enlightenment and entertainment.
In this moment variation, influenced via fresh lectures at Oxford, extra fabric and additional illustrations were additional on many issues together with colored Cubes, Chaos and Crystals.
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Extra resources for Gems of Geometry
Sample text
4} also uses three different polygons but maybe looks a little cluttered; however, it has a simple beauty because it can be looked upon as simply overlapping dodecagons (the Greek prefix for twelve is dodeca-). Two further patterns can be formed out of triangles and squares. Both have three triangles and two squares at each point but arranged in a different order. That on the left above is curious because it is so obviously different in the two directions whereas the other patterns are not. That on the right looks at first sight like an incoherent mess.
Underneath each pattern in the diagram below is shown its Schläfli symbol which consists of the symbol for the tile followed by the number of them around each point. Tiling with squares is commonplace in the kitchen and bathroom. The use of hexagons is familiar from the honeycomb made by bees and is also used in wire netting; it has the property of using least material (wax or wire for a given area or gauge size). 12} arranged as a hexagonal tiling. The triangle pattern is used for planting orchards since it gives the biggest distance between individual trees.
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. 4} known as the rhombicuboctahedron. Both the truncated icosidodecahedron and the rhombicosidodecahedron have 30 square faces and these are oriented in exactly the same way as the 30 faces of the compound of five cubes inscribed inside a dodecahedron which we met earlier. 6} which it may be remembered came in enantiomorphic forms (like left- and right-handed gloves).