Mathematical Labyrinths. Pathfinding: 22 (Problem Solving in Mathematics and Beyond)

Description

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. Contents Preface About the Author 1. Entering the Labyrinth 2. What? How? Why? A Detective Story 3. The Clue is in the Question 4. Thinking Outside the Box. Sophisms and Paradoxes 4.1 Playing Logical Games 4.2 Sophisms 4.3 Paradoxes 5. “Precise Steps” Problems. Playing Preferans 6. Euclidean Plane Transformations 6.1 Isometric Transformations 6.2 Homothety 7. Geometrical Constructions with Restricted Elements 8. Inventing a Problem 8.1 Inventing New Problems by Modifying a Solved Problem 8.2 Inventing New Problems by Analogy 8.3 Extending a Problem 9. Related Problems 9.1 Problems Relying on the Same Property 9.2 Restating a Problem 9.3 Converse Problems 9.4 Making a “Prognosis”. Generalizations 10. Alternative Solutions Search 11. Eureka! 11.1 Weighing Problems 11.2 Playing with Numbers 11.3 Equations to the Rescue 11.4 Recreational Geometry — Can You Do It? 11.5 Sense of Humor, Common Sense, and a Little Bit of Logic 11.6 Final Problem — Moral Test Solutions and Answers to Problems Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Final Problem — Moral Test Bibliography Index