Nonplussed!: Mathematical Proof of Implausible Ideas

Math-the application of reasonable logic to reasonable assumptions-usually produces reasonable results. But sometimes math generates astonishing paradoxes-conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true. Did you know that a losing sports team can become a winning one by adding worse players than its opponents? Or that the thirteenth of the month is more likely to be a Friday than any other day? Or that cones can roll uphill?...