Mathematical Labyrinths. Pathfinding provides an overview of various non-standard problems and the approaches to their solutions.
Mathematical Labyrinths. Pathfinding provides an overview of various non-standard problems and the approaches to their solutions. The essential idea is a framework laid upon the reader on how to solve nonconventional problems — particularly in the realm of mathematics and logic. It goes over the key steps in approaching a difficult problem, contemplating a plan for its solution, and discusses set of mental models to solve math problems.The book is not a routine set of problems. It is rather an entertaining and educational journey into the fascinating world of mathematical reasoning and logic. It is about finding the best path to a solution depending on the information given, asking and answering the right questions, analyzing and comparing alternative approaches to problem solving, searching for generalizations and inventing new problems. It also considers as an important pedagogical tool playing mathematical and logical games, deciphering mathematical sophisms, and interpreting mathematical paradoxes.It is suitable for mathematically talented and curious students in the age range 10–20. There are many 'Eureka'- type, out of the ordinary, fun problems that require bright idea and insight. These intriguing and thought-provoking brainteasers and logic puzzles should be enjoyable by the audience of almost any age group, from 6-year-old children to 80-year-old and older adults.
| Preface |
|
vii | |
| About the Author |
|
xiii | |
|
|
|
1 | (22) |
|
|
|
23 | (28) |
|
3 The Clue is in the Question |
|
|
51 | (18) |
|
4 Thinking Outside the Box. Sophisms and Paradoxes |
|
|
69 | (20) |
|
5 "Precise Steps" Problems. Playing Preferans |
|
|
89 | (16) |
|
6 Euclidean Plane Transformations |
|
|
105 | (20) |
|
7 Geometrical Constructions with Restricted Elements |
|
|
125 | (18) |
|
|
|
143 | (28) |
|
|
|
171 | (28) |
|
10 Alternative Solutions Search |
|
|
199 | (28) |
|
|
|
227 | (14) |
| Solutions and Answers to Problems |
|
241 | (60) |
| Bibliography |
|
301 | (4) |
| Index |
|
305 | |
Kiev, Ukraine native Boris Pritsker worked as a math teacher in a special school for gifted and talented high school students with advanced programs in algebra, geometry, trigonometry, and calculus. His teaching experience led to his publication of numerous articles and problems in mathematical magazines in the former Soviet Union, United States, Australia, and Singapore. He published two books, Geometrical Kaleidoscope, Dover Publications, Inc., 2017 and The Equations World, Dover Publications, Inc., 2019. Both books are featured with positive reviews at Mathematical Association of America website. The MAA's Basic Library List Committee assigned the BLL rating to "Geometrical Kaleidoscope" and suggested that undergraduate mathematics libraries consider the book for acquisition.
Lisainfo e-raamatute kohta