Research in History and Philosophy of Mathematics 1st edition by Maria Zack, Elaine Landry ISBN 3319222570 978-3319222578
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ISBN 10: 3319222570
ISBN 13: 978-3319222578
Author: Maria Zack, Elaine Landry
This volume contains thirteen papers that were presented at the 2014 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d’Histoire et de Philosophie des Mathématiques, held on the campus of Brock University in St. Catharines, Ontario, Canada. It contains rigorously reviewed modern scholarship on general topics in the history and philosophy of mathematics, as well as on the meeting’s special topic, Early Scientific Computation. These papers cover subjects such as •Physical tools used by mathematicians in the seventeenth century •The first historical appearance of the game-theoretical concept of mixed-strategy equilibrium •George Washington’s mathematical cyphering books •The development of the Venn diagram •The role of Euler and other mathematicians in the development of algebraic analysis •Arthur Cayley and Alfred Kempe’s influence on Charles Peirce’s diagrammatic logic •The influence publishers had on the development of mathematical pedagogy in the nineteenth century •A description of the 1924 International Mathematical Congress held in Toronto, told in the form of a “narrated slide show” Written by leading scholars in the field, these papers will be accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.
Research in History and Philosophy of Mathematics 1st 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
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