What's in Convergence? - Contents of Volume 16 - 2019

Editors:  Amy Ackerberg-Hastings, Janet Heine Barnett, Janet Beery (through 1/31/19)

Associate Editors:  Paul Bialek, Eugene Boman, Maureen Carroll, Lawrence D'Antonio, Sloan Despeaux, Victor Katz (through 1/31/19), Michael Molinsky, Elyn Rykken, Randy Schwartz, Amy Shell-Gellasch, Jody Sorensen, Gary Stoudt, Erik R. Tou, Laura Turner

Founding Editors: Victor Katz, Frank Swetz

Articles

Correspondence from Mathematicians by Jennifer Horn, Amy Zamierowski and Rita Barger (posted 12/30/2019)
A project designed by the co-authors to provide their students with a research experience that helped them discover the origins of familiar mathematical concepts.

An Explication of the Antilogism in Christine Ladd-Franklin's "Algebra of Logic" by Julia M. Parker (posted 12/12/2019)
An overview of Ladd-Franklin's contributions to symbolic logic, based on an explication of an excerpt from her doctoral dissertation.

Bringing Historical Methods for Astronomical Measurements into the Classroom by Seán P. Madden, Jocelyne M. Comstock, and James P. Downing (posted 10/14/2019)
Student activities that combine data collection with astronomical measurement methods attributed to Eratosthenes, Ptolemy, and Galileo.

Here's Looking at Euclid by Sid Kolpas and Stu Ockman (posted 09/16/2019)
A mathematical crossword puzzle with historical overtones.

To Simplify, or Not To Simplify? A Lesson from Medieval Iraq by Valerio De Angelis and Jeffrey A. Oaks (posted 09/02/2019)
A case where not simplifying fractions explains a curious rule for computing cube roots from medieval Arabic mathematics, with student exercises.

MAA Convergence is Sweet Sixteen!
As Convergence marks its 16th volume, we recognize its long-term former editors by compiling their contributions to the journal’s content and by presenting a brief history of the journal.

• Celebrating Frank Swetz (2004–2009, also founding co-editor)
  • Do We Teach Too Much Mathematics . . . ? A new essay on the justifications for using history to teach mathematics.
• Celebrating Victor Katz (2004–2009, also founding co-editor)
• Celebrating Janet Beery (2009–2019)
• A Brief History of Convergence

Servois' 1817 "Memoir on Quadratures" translated by Robert E. Bradley and Salvatore J. Petrilli, Jr. (posted 05/20/2019)A readers' guide and complete English translation of Servois' 1817 contribution to a debate on numerical integration.

HOM SIGMAA 2019 Student Paper Contest Winner (posted 04/23/2019)Read the winning entry, "Omar Khayyam's Successful Replacement of Euclid's Parallel Postulate" by Amanda Nethington, from the 16th annual edition of this contest.

Teaching Mathematics with Ephemera: John Playfair's Course Outline for Practical Mathematics by Amy Ackerberg-Hastings (posted 04/22/2019)
Ephemera are a category of primary source that may prove especially engaging for students. The article provides examples of ephemera, a sample analysis of one piece of ephemera, and suggestions for incorporating this form of primary source into mathematics classrooms.

Using the Publimath Database to Bring History into our Teaching by Hombeline Languereau and Anne Michel-Pajus (posted 04/08/2019)
Description, with user instructions, of a French online resource cataloging research articles and projects for using history to teach mathematics.

More Than Just a Grade: The HOM SIGMAA Student Contest Fosters Writing Excellence at UMKC by Richard Delaware (posted 02/10/2019)
Advice on promoting excellence in student research and writing in the history of mathematics.

Ongoing Series

A Series of Mini-projects from TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources, by Janet Barnett, Kathy Clark, Dominic Klyve, Jerry Lodder, Danny Otero, Nick Scoville, and Diana White

• Series Introduction, by Janet Barnett, Kathy Clark, Dominic Klyve, Jerry Lodder, Daniel E. Otero, Nick Scoville, and Diana White
• The Derivatives of the Sine and Cosine Functions: A Mini-Primary Source Project for Calculus 1, by Dominic Klyve
• Why be so Critical? Nineteenth Century Mathematics and the Origins of Analysis: A Mini-Primary Source Project for Introductory Analysis Students, by Janet Heine Barnett
• Connecting Connectedness: A Mini-Primary Source Project for Topology Students, by Nicholas A. Scoville
• Generating Pythagorean Triples: A Mini-Primary Source Project for Mathematics Majors, Elementary Teachers and Others, by Janet Heine Barnett
• Euler's Rediscovery of e: A Mini-Primary Source Project for Introductory Analysis Students, by Dave Ruch
• How to Calculate \(\pi\): Machin's Inverse Tangents, A Mini-Primary Source Project for Calculus 2 Students, by Dominic Klyve
• Henri Lebesgue and the Development of the Integral Concept: A Mini-Primary Source Project for Undergraduate Analysis Students, by Janet Heine Barnett
• Seeing and Understanding Data: A Mini-Primary Source Project for Students of Statistics, by Charlotte Bolch and Beverly Woods
• The Origin of the Prime Number Theorem: A Primary Source Project for Number Theory Students, by Dominic Klyve
• The Cantor Set Before Cantor: A Mini-Primary Source Project for Analysis and Topology Students, by Nicholas A. Scoville
• Euler’s Calculation of the Sum of the Reciprocals of the Squares: A Mini-Primary Source Project for Calculus 2 Students, by Kenneth M Monks
• Completing the Square: From the Roots of Algebra, A Mini-Primary Source Project for Students of Algebra and Their Teachers, by Daniel E. Otero
• Regression to the Mean: A Mini-Primary Source Project for Statistics Students, by Dominic Klyve

Math Origins, by Erik R. Tou
How were concepts, definitions, and theorems familiar to today's students of mathematics developed over time?

• Math Origins: The Totient Function
• Math Origins: Orders of Growth
• Math Origins: Eigenvectors and Eigenvalues
• Math Origins: The Logical Ideas
• Math Origins: The Logical Symbols

Mathematical Treasures

Mathematical Treasures at the Linda Hall Library, by Cynthia J. Huffman Description of the physical and digital history of science collections of the Linda Hall Library in Kansas City. At least 75 of LHL's digitized rare books relate to the history of mathematics and can be used in classrooms.

Mathematical Treasures from the Linda Hall Library added during 2019:

• Gregor Reisch's Margarita Philosophica (1517, original 1503)
• Jacob Köbel's Geometrei (1535)
• Raphael Bombelli’s L'algebra parte maggiore dell’aritmetica divisa in tre libri (1579, original 1572)
• Bernard de Fontenelle's A Panegyric upon Sir Isaac Newton (1728 English translation)
• James Jurin's A Defence of Sir Isaac Newton (1734)

• Robert Simson’s Sectionum Conicarum (1735)

• Abraham De Moivre’s Doctrine of Chances (1738, original 1711/1718)

• Robert Simson’s The Elements of Euclid (1756)

• Robert Simson's Opera Quaedam Reliqua (1776)

• Joseph-Louis Lagrange's Traité de la Résolution des Equations Numérique (1808 revision of 1798 original)

Mathematical Treasures, by Frank J. Swetz

Index to Mathematical Treasures Collection: Images of historical texts and objects from libraries, museums, and individuals around the world for use in your classroom!

Mathematical Treasures added during 2019:

• Egyptian Wooden Codex (6th or 7th century)
• Gerbert's Geometriae (12th century copy of c. 1000 CE original)
• Sphaera Mundi of Abraham bar Hiyya (1546, original 11th or 12th century)
• Adelard's Translation of Euclid's Elements (12th-14th centuries)
• Sacrobosco's Sphaera mundi (c. 1256-1270 manuscript)
• Isadore of Seville's Etymologiae (c. 1265)
• Liber abaci of Leonardo of Pisa (14th-cent. copy of 1202 original)
• John Peckham's Perspectiva (1556, original 13th century)
• Muscarello's Algorismus from Southern Italy (c. 1478)
• The Arithmetic of Piero Borghi​ (1491, original 1484)
• Luca Pacioli's Summa de arithmetica, geometria, …  (1494)
• Arithmetic of Juan Martinez Siliceo​ (1514) 
• First Printed Greek Euclid's Elements (1533) 
• Johannes Stöffler's Art of Measurement (1536)
• Arithmeticae practicae of Gemma Frisius (1540/1567)
• Oronce Fine's De mundi sphaera (1542)
• Ptolemaei mathematicae (Almagest in Greek/Latin, 1549)
• Charles de Bovelles's Practical Geometry (1555)
• Robert Recorde's Castle of Knowledge (1556)
• First Euclid's Elements in Greek and Latin (1558)
• Scholarum mathematicarum of Peter Ramus (1559)
• Juan de Ortega's Tractado Subtilissimo d’arismetica  (1563)
• Pietro Cataneo's Le pratiche della due prime matematiche … (Practice of the two basic Mathematics) (1567)
• First Spanish Euclid's Elements (1576)
• Danti on Euclid's Optics (1573) and the Astrolabe (1578)
• Marchesi's Handbook of Commercial Arithmetic (1578)
• al-Tusi's printed Arabic edition of Euclid's Elements (1594)
• Van Ceulen's ​On the Circle (1596)
• Peurbach's New Theory of the Planets (c. 16th century)
• Guidobaldo del Monte's Perspectiva (1600)
• Tycho Brahe's Astronomiae instauratae mechanica (1602)
• Galileo's Siderius nuncias with author's signature (1610)
• Two Portraits of John Napier (1550-1617)
• John Napier,  A Declaration of the Admirable Table of Logarithmes  (1618)
• Kepler's Harmony of the Worlds (1619)
• Metius on Geography and Measurement (1624)
• Adriaan Vlacq's Arithmetique Logarithmetique (1628)
• Student notes from lectures of Rhodius, University of Wittenberg (1629)
• Samuel Marolois's three volumes: Geometria, Fortification, and Perspectiva (1629)
• Christoph Scheiner's pantograph and sunspot device (1631)
• Marginal note by Galileo in his Dialogue (1632)
• Philip Lansberge's Astronomical Tables (1632)
• Philip Lansberge's Quadrant (1635)
• Letter from Torricelli to Mersenne (1645)
• Riccioli's New Almagest (1651)
• Mathematical Works of Caroli Rinaldini (1655)
• John Wallis's De Sectionibus Conicis (1655) and ​Arithmetica Infinitorum (1656)
• Graunt's Early Statistics on Mortality (1662)
• Cardinal Ricci on Maxima & Minima (1668)
• van Schooten's Latin edition of Descartes's Geometry (1683, original 1649)
• Seth Partridge's Double Scale Slide Rule (1692)
• De Locis Solidis of Vincenzo Viviani (1701)
• Edward Hatton's The Merchant’s Magazine or Trades Man’s Treasury (1707, original 1701)
• Works of Isaac Newton (1711) 
• James Hodder's Arithmetick (1719, original 1661)
• Colin Maclaurin's Geometria Organica (1720)
• John Keill's Euclid's Elements and other works (1723/1782)
• Girolamo Saccheri's Euclid Vindicated of All Errors (1733)
• L’Abbé Deidier's L’Arithmetique des Géométres (1739)
• Newton's Fluxions owned by De Morgan (1740)
• Critical Edition of Newton's Principia (1739–1742)
• John Stewart's early text based on Newton's calculus (1745)
• Signature and portrait of Colin Maclaurin (early 18th century, 1814), contributed by Sid Kolpas
• Gabriel Cramer's Introduction a l’Analyse des Lignes Courbes Algebriques (1750)
• Juan Bautista Corachán's Arithmetic for Merchants (1757, original 1699) 
• Benjamin Franklin's "Magic Square of Squares" discussed in Gentleman's Magazine (1768), contributed by Sid Kolpas
• Two Works of Joseph Fenn (1769/1772)
• Of the Parabola (late 18th century)
• Euler's Institutiones Calculus Differentialis (1787)
• Georg Vega's Lectures on Applied Mathematics (1788, 1819)
• Chauncey Lee's The American Accomptant (1797), contributed by Sid Kolpas
• Charles Bossut's Cours de Mathématiques (1800)
• Lazare Carnot on Infinitesimal Calculus (1797) and Geometry (1801)
• Francis Maseres's Resolution of Cubick and Biquadratic Equations (1803)
• N. R. Tomlinson's ciphering book from the Royal [Naval] Academy, Portsmouth (1806)
• Joseph Nicolas Nicollet's Traité elémentaire [et] synthétique des sections coniques (1809)
• Pierre-Simon Laplace's Théorie Analytique des Probabilités (1812)
• John Graham's The Farmers’ and Mechanics’ Assistant or Companion, or A New System of Decimal Arithmetic (1824)
• Abraham Lincoln's Cipher Book (ca. 1825)
• Works of Siméon-Denis Poisson (1831/1833/1835)
• First Edition of Liouville's Journal (1836)
• Liouville's Journal de Mathématiques Pures et Appliquées (founded 1836)
• Augustus De Morgan's "Induction (Mathematics)" (1838), contributed by Sid Kolpas
• John Napier's De Arte Logistica (1839)
• Nicholas Lobachevsky's Theorie der Parallellinien (1840)
• Ada Lovelace's Notes on the Analytic Engine (1843)
• Bernhard Riemann's Inaugural Address at Göttingen (1854/1867)
• Works of Charles Hermite (1873/1885/1905)
• George Boole on the Laws of Thought (1874)
• Letter by Florence Nightingale (1875), contributed by Anna Bargagliotti and Rebecca Nichols
• Weierstrass lecture notes (1879-1881)
• First issue of Acta Mathematica with Poincáre's Théorie des Groupes Fuchsiens (1882)
• Works of Paul du Bois-Reymond (1887/1912)
• Herman Hollerith's tabulating machine discussed in Scientific American (1890), contributed by Sid Kolpas
• Works of Paul Bachmann (1892/1894/1925)
• Lewis Carroll's Symbolic Logic (1896)
• Postcard written by Charles Dodgson (aka Lewis Carroll, 1896), contributed by Sid Kolpas
• Henry F. Baker's Abel's Theorem and Allied Theory (1897)
• Oeuvres mathématiques de Riemann (1898)
• Collected Mathematical Papers of J. J. Sylvester (1904)
• Henri Lebesgue's Leçons sur l'intégration (1904)
• G. H. Hardy's Orders of Infinity (1910)
• Bonola's Non-Euclidean Geometry (1912)
• Works of Hermann Weyl (1913/1918/1919)
• Albert Einstein's paper on Riemannian geometry (1928) 
• Henry F. Baker's Principles of Geometry (1929/1933)
• Bruce Rogers’s Elements of Geometry Book I (1944), contributed by Sid Kolpas