Numbers and Shapes Revisited: More Problems for Young Mathematicians

ISBN : 9780198534600

Judita Cofman
320 Pages
156 x 233 mm
Pub date
Mar 1995
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Mathematics is primarily concerned with problem solving, and there is no better way of gaining an understanding of mathematics than by developing the independent thinking and ability to solve problems (and to set them). The mathematics syllabuses in today's secondary schools contain a wide range of notions and basic facts from various mathematical disciplines. Pupils interested in mathematics should be encouraged to explore the connections between the different topics they encounter, and this book attempts to help in pointing out these connections. By focusing attention on the links between patterns of numbers and shapes, and on between algebraic relations and geometric and combinatorial configurations, the book aims to * motivate deeper study of the concepts related to elementary mathematics * emphasize the importance of the interrelations between mathematical phenomena * foster the interplay of ideas involved in problem solving The material is presented in the form of problems and will prove invaluable and enjoyable for pupils, their teachers, and those studying mathematics or its teaching at university.


1. The Fibonacci sequence, generalized Fibonacci sequences, and related topics
2. Patterns of dots and partitions of integers
3. Patterns, related to rational numbers: periodic decimal fractions, repunits, and visible lattice points
4. Reflected light rays and real numbers: a theorem of Kronecker
5. The Chinese remainder theorem and invisible lattice points
6. Two famous inequalities and some related problems
7. "Mysteries" of the their dimension: on cubes, pyramids, and spheres
8. A Glimpse of higher-dimensional spaces: hypercubes, lattice paths, and related number patterns
9. Do it with groups
10. From puzzles to research topics: selected problems of combinatorics

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