Two, Three, Four, and More: The Mathematically Special Dimensions

A beautifully illustrated exploration of the remarkable world of mathematics in low dimensionsHighly valued results in mathematics are often general: proofs in all dimensions, solutions for all degrees of polynomials.Yet great richness can be found in particular cases.John Stillwell presents a visual panorama of the multitudes that live in dimensions 2, 3, and 4-and a few higher dimensions-through the interplay of geometry, topology, and algebra. We tend to think of the dimensions 2, 3, and 4 as the dimensions of our physical experience in space and time, but they are also of exceptional mathematical interest.Together with the degrees 2, 3, and 4 of equations, they cover some of the most remarkable mathematical objects and pose problems ranging from easy, to hard, to unsolvable.Each chapter of this engaging book focuses on a dimension or degree, starting at 2 dimensions and ascending to 4 dimensions and then beyond to objects such as the Leech lattice in 24 dimensions.The gradual incre