By John Barnes

In accordance with a sequence of lectures for grownup scholars, this energetic and enjoyable booklet proves that, faraway from being a dusty, uninteresting topic, geometry is actually choked with attractiveness and fascination. The author's infectious enthusiasm is positioned to exploit 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, winding up 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' booklet is the proper 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 bewilderment and frustration, Barnes brings enlightenment and leisure.

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A linguistic interlude might be in order. The word polygon comes from two Greek words, πολυς (polus), many and γονος (gonos), angled. The individual names such as pentagon use the Greek number prefixes, penta-, hex-, hept-, octand so on. English is curious, sometimes numbers are taken from the Greek as here but sometimes from Latin as in quartet, quintet, sextet. One might think that these regular figures were the end of the story but we can consider another way of looking at their construction.

If we slice a small corner off a cube, then the revealed section is a triangle since three edges and faces meet at a corner of the cube. We say that the vertex figure of a cube is a triangle. Strictly speaking the vertex figure is defined as that formed by joining the midpoints of the edges meeting at the vertex. The Schläfli symbol for a polyhedron is properly interpreted as the symbol for its face followed by that for its vertex figure. So the cube has Schläfli symbol {4, 3}, that of the tetrahedron is {3, 3), the octahedron is {3, 4}, the icosahedron is {3, 5} and the beautiful dodecahedron is {5, 3}.

2 Shapes and Solids 45 Great stellated dodecahedron {5/2, 3} Great icosahedron {3, 5/2} The Kepler–Poinsot figures with density 7. The small stellated dodecahedron appears in Escher’s lithographs, Order and Chaos (two versions) and Gravity. It has also been used as the basis for glass lanterns. The great icosahedron is somewhat confusing; its triangular faces do not stand out clearly since they are penetrated by three vertex figures. However, the great dodecahedron is very attractive; both the pentagonal faces and the vertex figures are immediately obvious.

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