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Foreword; Preface; Contents; About the Authors; Part I: Setting the Scene; Chapter 1: Introduction to the Book; 1.1 Introduction; 1.2 The Purpose and Scope of This Book; 1.3 What Is a Tool?; 1.3.1 Johnś Attempt to Address This Question; 1.3.2 Lucś Attempt to Address This Question; 1.4 The Structure of the Book; References; Chapter 2: Doing Mathematics with Tools: One Task, Four Tools; 2.1 Introduction; 2.2 Bisecting an Angle with a Straight Edge and a Compass; 2.3 Bisecting an Angle with a Protractor; 2.4 Bisecting an Angle with a Dynamic Geometry System; 2.5 Bisecting an Angle with a Book
Chapter 3: The Life of Modern Homo Habilis Mathematicus: Experimental Computation and Visual Theorems3.1 Introduction; 3.1.1 Who I Am and How I Got That Way; 3.1.2 What Follows; 3.1.3 Some Early Conclusions; 3.2 Visual Theorems and Experimental Mathematics; 3.2.1 Visual Theorems; 3.2.2 On Picture-Writing; 3.2.2.1 Proofs Without Words; 3.3 Experimental Mathematics; 3.3.1 Experimental Mathodology; 3.3.2 When Science Becomes Technology; 3.3.2.1 Minimal Configurations; 3.3.3 Mathematical Discovery (or Invention); 3.3.4 Digital Assistance; 3.3.5 The Twentieth Centuryś Top Ten Algorithms
3.3.6 Secure Knowledge Without Proof3.3.7 Is `Free ́Software Better?; 3.4 A Dozen or So Accessible Examples; 3.5 Simulation in Pure Mathematics; 3.5.1 Monte Carlo Simulation of pi; 3.5.2 Finding a Region of Convergence; 3.6 Case Studies I: Dynamic Geometry; 3.6.1 Case Study Ia: Iterative Reflections; 3.6.2 Case Study Ib: Protein Conformation; 3.7 Case Studies II: Numerical Analysis; 3.7.1 Case Study IIa: Trefethenś 100 Digit Challenge; 3.7.2 Case Study IIb: Algorithms for Polylogarithms; 3.8 Case Studies III: Randomish Walks; 3.8.1 Case Study IIIa: Short Walks; 3.8.1.1 The Three-Step Walk
3.8.1.2 The Four-Step Walk3.8.2 Case Study IIIb: Number Walks; 3.8.3 Case Study IIIc: Normality of Stoneham Numbers; 3.9 Conclusion; References; Chapter 4: Tools, Human Development and Mathematics; 4.1 Introduction; 4.2 Tool Use and Phylogenesis; 4.3 Ancient Greece; 4.3.1 Discussion of This Proof; 4.3.2 Tools; 4.3.3 Oral and Written Mathematics; Communities of Practice; 4.4 Ancient Indian Square Roots; 4.5 Abaci; 4.6 Tools for Calculation in Europe Circa 1600; 4.7 Discussion: Insights on Tool Use Over Time; References
Chapter 5: The Development of Mathematics Practices in the Mesopotamian Scribal Schools5.1 Introduction; 5.2 A Critical Moment; 5.3 The Computation Practices and Their Support in Scribal Schools; 5.4 Evidencing Computing Artefacts Complementing the Usage of Tablets and Memory; 5.5 Analysing the Algorithm for Calculating a Reciprocal, a Way for Entering the Spirit of Mesopotomian Computation; ; 5.6 Conclusion and Discussion; References; Chapter 6: Discussions of Part I Chapters; 6.1 Introduction; 6.2 Interactions with John and Jon Follow-Up; 6.2.1 Writing and Mathematics, a Dual Invention?
Chapter 3: The Life of Modern Homo Habilis Mathematicus: Experimental Computation and Visual Theorems3.1 Introduction; 3.1.1 Who I Am and How I Got That Way; 3.1.2 What Follows; 3.1.3 Some Early Conclusions; 3.2 Visual Theorems and Experimental Mathematics; 3.2.1 Visual Theorems; 3.2.2 On Picture-Writing; 3.2.2.1 Proofs Without Words; 3.3 Experimental Mathematics; 3.3.1 Experimental Mathodology; 3.3.2 When Science Becomes Technology; 3.3.2.1 Minimal Configurations; 3.3.3 Mathematical Discovery (or Invention); 3.3.4 Digital Assistance; 3.3.5 The Twentieth Centuryś Top Ten Algorithms
3.3.6 Secure Knowledge Without Proof3.3.7 Is `Free ́Software Better?; 3.4 A Dozen or So Accessible Examples; 3.5 Simulation in Pure Mathematics; 3.5.1 Monte Carlo Simulation of pi; 3.5.2 Finding a Region of Convergence; 3.6 Case Studies I: Dynamic Geometry; 3.6.1 Case Study Ia: Iterative Reflections; 3.6.2 Case Study Ib: Protein Conformation; 3.7 Case Studies II: Numerical Analysis; 3.7.1 Case Study IIa: Trefethenś 100 Digit Challenge; 3.7.2 Case Study IIb: Algorithms for Polylogarithms; 3.8 Case Studies III: Randomish Walks; 3.8.1 Case Study IIIa: Short Walks; 3.8.1.1 The Three-Step Walk
3.8.1.2 The Four-Step Walk3.8.2 Case Study IIIb: Number Walks; 3.8.3 Case Study IIIc: Normality of Stoneham Numbers; 3.9 Conclusion; References; Chapter 4: Tools, Human Development and Mathematics; 4.1 Introduction; 4.2 Tool Use and Phylogenesis; 4.3 Ancient Greece; 4.3.1 Discussion of This Proof; 4.3.2 Tools; 4.3.3 Oral and Written Mathematics; Communities of Practice; 4.4 Ancient Indian Square Roots; 4.5 Abaci; 4.6 Tools for Calculation in Europe Circa 1600; 4.7 Discussion: Insights on Tool Use Over Time; References
Chapter 5: The Development of Mathematics Practices in the Mesopotamian Scribal Schools5.1 Introduction; 5.2 A Critical Moment; 5.3 The Computation Practices and Their Support in Scribal Schools; 5.4 Evidencing Computing Artefacts Complementing the Usage of Tablets and Memory; 5.5 Analysing the Algorithm for Calculating a Reciprocal, a Way for Entering the Spirit of Mesopotomian Computation; ; 5.6 Conclusion and Discussion; References; Chapter 6: Discussions of Part I Chapters; 6.1 Introduction; 6.2 Interactions with John and Jon Follow-Up; 6.2.1 Writing and Mathematics, a Dual Invention?