Research in History and Philosophy of Mathematics 1st Edition by Maria Zack, Dirk Schlimm ISBN 9783030952006 3030952002

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ISBN 10: 3030952002
ISBN 13: 9783030952006
Author: Maria Zack, Dirk Schlimm

Research in History and Philosophy of Mathematics 1st Edition Table of contents:

Falconer’s Cryptology

1 Introduction

2 Dating Falconer’s Work

2.1 References Within Cryptomenysis

2.2 Motivation for Cryptomenysis

2.3 Falconer’s Biography

3 Contents of Cryptomenysis

3.1 Overview

3.2 Specific Examples

4 Conclusion

References

Is Mathematics to Be Useful? The Case of de la Hire, Fontenelle, and the Epicycloid

1 Introduction

2 Background in Mathematics and Mechanics

3 La Hire and Fontenelle on the Epicycloid

4 A Sign of the Times

References

The Rise of “the Mathematicals”: Placing Maths into the Hands of Practitioners—The Invention and

1 Introduction

2 The Importance of Proportional Analogies in General Problem Solving

3 Description and Use of the Lines of the Sector

3.1 Line of Lines

3.2 Line of Superficies

3.3 Lines of Circular Parts

3.4 The Particular Lines

3.4.1 The Lines of Quadrature

3.4.2 The Lines of Segments

3.4.3 The Lines of Inscribed Bodies and the Line of Equated Bodies

3.4.4 The Lines of Metals

4 Logarithmic Scales and Rules

5 Construction and Use of the Scales of the Gunter’s Rule

5.1 Construction of Lines of Equal Parts

5.2 Construction of Circular Lines

5.3 Construction of Lines of Superficies

5.4 Construction of Logarithmic Lines

6 Three Applications from Astronomy: Solutions by Sector and Scale Compared

6.1 Problem 1: Given the Distance of the Sun from the Equinoctial Point, to Find Its Declination

6.2 Problem 2: Given the Latitude of Your Location and the Sun’s Declination at Sunrise, to Find Azi

6.3 Problem 3: Given the Latitude of Your Location, Declination of the Sun, and the Sun’s Altitude,

7 Impact of Sectors and Scales on Mathematics, Science, and Society

8 Credits

References

Early Modern Computation on Sectors

1 The History of Sectors According to NMAH

2 Sectors in the Italian Style

3 Sectors in the French Style

4 Sectors in the English Style

5 Conclusion

References

The Eighteenth-Century Origins of the Concept of Mixed-Strategy Equilibrium in Game Theory

1 Introduction

2 Le Her and Its Solution

3 Jouer au Plus Fin

Appendix 1: Calculating Paul’s Winning Card Counts

Appendix 2: Calculating Paul’s Advantage

References

Reassembling Humpty Dumpty: Putting George Washington’s Cyphering Manuscript Back Together Again

1 Introduction

2 Provenance of the Manuscript

3 A Page That the Library of Congress Did Not Digitize

4 The Cornell Leaf

5 The Dartmouth Leaf

6 A Leaf at the Historical Society of Pennsylvania

7 A Missing Leaf

8 Conclusion

References

Natures of Curved Lines in the Early Modern Period and the Emergence of the Transcendental

1 Introduction

2 Known and Nature in Early Modern Mathematics

3 Pappus: Plane, Solid, and Line-Like Curved Lines

4 Descartes: Geometrical and Mechanical Curved Lines

5 Euler: Algebraic and Transcendental Curved Lines

6 Conclusion

References

Origins of the Venn Diagram

1 Introduction

2 Early Influences

3 Leibniz

4 Euler

5 Venn

References

Mathematics for the World: Publishing Mathematics and the International Book Trade, Macmillan and Co

1 Introduction

2 John Charles Fields’ Mathematical Studentship

3 Isaac Todhunter’s Mathematical Textbooks

4 Publishing and the History of Mathematics

5 Macmillan and Company as a Mathematical Publisher

6 Book Trade Influence: Research Monographs Versus Textbooks

A.1 Appendix 1: Isaac Todhunter’s Publications with Macmillan, 1843–1889

A.2 Appendix 2: Macmillan’s Mathematical Books with Print Runs Greater Than 100,000, 1843–1889

References

The Influence of Arthur Cayley and Alfred Kempe on Charles Peirce’s Diagrammatic Logic

1 Introduction

2 Peirce’s Entitative Graphs

3 The Development of Existential Graphs

4 Arthur Cayley’s Influence on Pierce

5 Alfred Bray Kempe

6 Conclusion

References

Émile Borel et Henri Lebesgue: HPM

1 Introduction: mathématiques et pédagogie au début du XXe siècle

2 Émile Borel : homme d’action

3 Émile Borel comme professeur : commentaires sur Les fonctions de variables réelles et les dével

4 Henri Lebesgue : l’homme

5 Henri Lebesgue comme professeur

6 Commentaires sur l’histoire des mathématiques dans les Leçons sur les séries trigonométriques

References

The Judicial Analogy for Mathematical Publication

1 Judicial Analogy

2 Testimony

References

History and Philosophy of Mathematics at the 1924 International Mathematical Congress in Toronto

1 Introduction

2 J. C. Fields and the Toronto IMC

3 The Schedule of the 1924 IMC

4 History, Philosophy, Didactics Section at the 1924 IMC

5 Four Leaders: Fehr, Cajori, Miller, Peano

5.1 Henri Fehr (1870–1954)

5.2 Florian Cajori (1859–1930)

5.3 George Abram Miller (1863–1951)

5.4 Giuseppe Peano (1858–1932)

6 Conclusion

References

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Tags: Maria Zack, Dirk Schlimm, History, Philosophy, Mathematics