The Art of Mathematics: Coffee Time in MemphisCambridge University Press, 14.09.2006 Can a Christian escape from a lion? How quickly can a rumour spread? Can you fool an airline into accepting oversize baggage? Recreational mathematics is full of frivolous questions where the mathematician's art can be brought to bear. But play often has a purpose. In mathematics, it can sharpen skills, provide amusement, or simply surprise, and books of problems have been the stock-in-trade of mathematicians for centuries. This collection is designed to be sipped from, rather than consumed in one sitting. The questions range in difficulty: the most challenging offer a glimpse of deep results that engage mathematicians today; even the easiest prompt readers to think about mathematics. All come with solutions, many with hints, and most with illustrations. Whether you are an expert, or a beginner or an amateur mathematician, this book will delight for a lifetime. |
Inhalt
Another Erdős Problem for Epsilons | 17 |
Planar Domains of Diameter 1 | 18 |
Orienting Graphs | 19 |
A Simple Clock | 20 |
Neighbours in a Matrix | 21 |
Separately Continuous Functions | 22 |
Boundary Cubes | 23 |
Lozenge Tilings | 24 |
Nested Subsets | 9 |
Almost Disjoint Subsets | 10 |
Loaded Dice | 11 |
An Unexpected Inequality | 12 |
the ErdősSelfridge Theorem | 13 |
Independent Sets | 14 |
Expansion into Sums | 15 |
A Tennis Match | 16 |
A Continuum Independent | 25 |
Separating Families of Sets | 26 |
Bipartite Covers of Complete Graphs | 31 |
the Theorems of Radon and Carathéodory | 33 |
Hellys Theorem | 35 |
Judicious Partitions of Points | 37 |
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a₁ Amer Angel angle antipodal points assertion assume bipartite graphs Bollobás Borsuk’s Claim closed sets colour combinatorial complete graph completing the proof conjecture Consequently contains contradiction convex sets cube define disjoint distance down-set edges Erdős-Ginzburg-Ziv theorem Figure finite set function G.H. Hardy Graph Theory Hence hexagon hypergraph hyperplane implies inequality infected sites infinite integer intersection k-subsets least length London Math lozenge Mathematics matrix maximal minimal number modulo n-dimensional natural numbers neighbours non-empty Notes number of elements odd number partition path Paul Erdős permutation plane polygonal polynomial prime problem prove random real number rectangles result segment sequence sets of diameter Show side-length solution Sperner family square-free strategy subgraph subsets summands Suppose Sylvester-Gallai theorem theorem triangle trivial unit square vectors vertex vertex set vertices write