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Sophisticated mathematics is accessible to all. This book proves it! This is a collection of intriguing mathematical problems and activities linked by common themes that all involve working with objects from our everyday experience. Learn about the mathematics of a bagel, a checkerboard and a pile of laundry for example. Discover for yourself that wheels need not be round, that braids need not have free ends, that it's always best to turn around twice - and more! Mathematics is all around us, we all do mathematics every day. The activities contained in this book are immediate, catchy and fun, but upon investigation, begin to unfold into surprising layers of depth and new perspectives. The necessary mathematics, in increasing levels of difficulty, is explained fully along the way. Mathematics educators will find this an invaluable resource of fresh and innovative approaches to topics in mathematics.
Part I. Activities, Discussions and Problem Statements: 1. Distribution dilemmas; 2. Weird shapes; 3. Counting on the odds … and evens; 4. Dicing slicing and avoiding bad bits; 5. 'Impossible' paper tricks; 6. Tiling challenges; 7. Things that won't fall down; 8. Möbius madness; tortuous twists on a classic theme; 9. The infamous bicycle problem; 10. Making surfaces in 3 and 4 dimensional space; 11. Paradoxes in probability theory; 12. Don't turn around just once; 13. It's all in a square; 14. Bagel math; 15. Capturing chaos; 16. Who has the advantage?; 17. Laundry math; 18. Get knotted; 19. Tiling and walking; 20. Automata antics; 21. Bubble trouble; 22. Halves and doubles; 23. Playing with playing cards; 24. Map mechanics; 25. Weird lotteries; 26. Flipped out; 27. Parts that do not add up to their whole; 28. Making the sacrifice; 29. Problems in parity; 30. Chessboard maneuvers; Part II. Hints, Some Solutions and Further Thoughts: Part III. Solutions and Discussions.