What's in Convergence? - Contents of Volume 14 - 2017

Editor:  Janet Beery

Associate Editors: Amy Ackerberg-Hastings, Janet Heine Barnett, Maureen Carroll, Lawrence D'Antonio, Victor Katz, Michael Molinsky, Elyn Rykken, Gabriela Sanchis, Randy Schwartz, Amy Shell-Gellasch, Jody Sorensen, Gary Stoudt, Erik R. Tou

Founding Editors: Victor Katz, Frank Swetz

Articles

Crossword Puzzle: Mathematicians from A to Z, by Sid Kolpas and Stu Ockman

Or, what happened when a mathematics professor and a professional crossword puzzle constructor became neighbors!

A Translation of Evangelista Torricelli's Quadratura Parabolae per novam indivisibilium Geometriam pluribus modis absoluta, by Andrew Leahy and Kasandara Sullivan

An English translation and study of a work representative of the seventeenth century infinitesimal methods introduced by Cavalieri.

Exploring Liu Hui's Cube Puzzle: From Paper Folding to 3-D Design, by Lingguo Bu

How your students can explore an ancient cube dissection using paper models, computer animations, and/or 3D printing!

Illustrating The Nine Chapters on the Mathematical Art: Their Use in a College Mathematics History Classroom, by Joel K. Haack

The author's experiences on an MAA Mathematical Study Tour to China can enhance your classroom, too.

The Method of the Scales in ibn al-Hāʾim's Book of Delights, by Randy K. Schwartz and Frank J. Swetz

See the “method of the scales” (double false position) in use in Kitāb al-nuzah (Book of Delights), by ibn al-Hāʾim.

Moses ibn Tibbon’s Hebrew Translation of al-Hassar's Kitāb al Bayān, by Jeremy I. Pfeffer

An exploration of Abu Bakr al-Hassar's influential work about arithmetic of fractions, Kitāb al Bayān wa-l-tadhkār (Book of Proof and Recall)

HOM SIGMAA 2017 Student Paper Contest Winners

Download the three winning papers from the 14th annual competition.

Impacts of a Unique Course on the History of Mathematics in the Islamic World, by Nuh Aydin

How this course has affected its instructor and students, and how you, too, can teach such a course!

Analysis and Translation of Raffaele Rubini's 1857 'Application of the Theory of Determinants: Note', by Salvatore J. Petrilli, Jr., and Nicole Smolenski

A compendium of early determinant theory offered in defense of "analytic" mathematics

The Mathematics of Levi ben Gershon in the Classroom, by Shai Simonson

Translation of "word problems" and estimates of square roots and of pi for use with your students

Trisecting an Angle Using Mechanical Means, by Keith Dreiling

Four methods in all by Hippias, Archimedes, and Nicomedes illustrated with interactive applets!

The Mathematical Cultures of Medieval Europe, by Victor J. Katz

Cultural influences on the mathematics of Islamic, Jewish, and Catholic scholars

Recreational Problems in Medieval Mathematics, by Victor J. Katz

Two problems that endured across time, space, and culture

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

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

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, by Cynthia J. Huffman

• Euclid's Elementa Geometricae, Ratdolt printing (1482)
• Luca Pacioli's Sūma de Arithmetica Geometria Proportioni & Proportionalita (1494)
• Luca Pacioli's Divina Proportione (1509)
• Luca Pacioli's Euclid's Elements (1509)
• Girolamo Cardano's Ars Magna (1545)
• Euclid's Elements of Geometry, Arabic translation, Medicean printing (1594)
• Bonaventura Cavalieri's Geometria indivisibilibus continuorum nova quadam ratione promota (1635)
• Galileo Galilei's Discourses and Mathematical Demonstrations Concerning Two New Sciences (1638 and 1730 English translation by Thomas Weston)
• Evangelista Torricelli's Opera Geometrica (1644)
• John Caswell's A Brief (but full) Account of the Doctrine of Trigonometry, Both Plain and Spherical (1685)
• Guillaume François Marquis de l’Hospital's Analyse des Infiniment Petits, Pour l’intelligence des lignes courbes (1696)
• Evangelista Torricelli's Lezione Accademiche (1715)
• George Berkeley's The Analyst; or a Discourse Addressed to an Infidel Mathematician (1734)
• Francesco Algarotti's Il newtonianismo per le dame (1737, 1738 French translation)
• Émilie du Châtelet's Institutions de Physique (1741 edition)
• Maria Agnesi's Instituzioni Analitiche (1748)
• Émilie du Châtelet's Principes Mathématiques (1759)
• Maria Agnesi's Analytical Institutions, trans. John Colson (1801)
• Fibonacci's Liber abaci, ed. Baldassarre Boncompagni (1857 edition)
• Fibonacci's Practica Geometriae, ed. Baldassarre Boncompagni (1857 edition)

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 2017:

• Mesopotamian Square Root Table (circa 1999-1800 BCE)
• Maya Numeration in the Dresden Codex (early 13th century)
• God, the Supreme Geometer (illuminated frontispiece) (13th century)
• Introduction to Pythagorean Arithmetic of Nicomachus (14th century)
• Fifteenth Century Division Practice
• Kitāb al-nuzah (Book of Delights) of ibn al-Hāʾim (1506-07 copy of c. 1400 work)
• Qāḍī Zāda's Sharḥ ashkāl al-ta'sīs (Commentary on Fundamental Theorems) (copied before 1612 from c. 1412-13 original)
• Qāḍī Zāda's Sharḥ ashkāl al-ta'sīs (Commentary on Forms of Foundation) (copied in 1714-15 from c. 1412-13 original)
• The Book of Michael of Rhodes (1434)
• Albert of Saxony's Tractatus proportionum (1477)
• Suma de la art de arismetica (1482)
• Piero Borghi's Qui comenza la nobel opera de arithmetic (1484)
• Luca Pacioli’s Summa de Arithmetica, Geometria, … (1494)
• Epitome of Ptolemy’s Almagest, by Peuerbach and Regiomontanus (1496)
• Tantrasangraha of Nilakantha (1501)
• Juan de Ortega's Tractado ... d’arismetica y de geometria (1512/1552)
• Spanish Mercantile Arithmetic (1515)
• Boethius' Arithmetic (1521)
• Jean Fernel's De proportionibus (1528)
• Oronce Fine's World Map (1534)
• Nicolo Tartaglia's Nova Scientia (1537)
• Land Surveys in the Codex Vergara (1539)
• Nicolo Tartaglia's Euclid (1543)
• Libro primero de aritmética algebraica (1552)
• Popular Spanish Arithmetic for Merchants (1564, original 1539)
• Nicolo Tartaglia's l'Arithmetique (1578 Fr. trans. of 1556 original)
• Juan Perez de Moya's Arithmetic and Algebra (1573 & 1609)
• Arithmetic, Algebra, and Bookkeeping (1565)
• Geometric Analysis of the Six Books of Euclid (1566)
• Los seis libros primeros dela geometria de Euclides (1576)
• Practical Geometry for Tailors (1589)
• Flower of Reason (Fiore de ragione) for Merchants (compiled 1538-1638)
• Al‐ʿĀmilī's Essentials of Arithmetic (circa 1600)
• Nicolaus Reimers' Algebra (1601)
• Thomas Osborne's Gift of Arithmetic for a Queen (1602)
• Tycho Brahe’s Astronomy (1602/03)
• Four Mathematical Works of Christopher Clavius (3 new images of Algebra, 1608)
• Johann Kepler's Gift of a Six-pointed Snowflake (1611)
• Kepler’s Harmony of the Worlds (Harmonices mundi) (1619)
• Explanation of Arithmetic from Timbuktu (early 17th century)
• Leurechon’s Mathematicall Recreations (1633)
• Petri's Reckoning and Cypher Book (1635)
• Bettini's Mathematical Apiary (1642)
• Arismetica for Merchants and Traders (1644)
• William Oughtred's The Key to the Mathematicks (English trans., 1647), contributed by Sid Kolpas
• ​Speidell's Spherical Geometry Manuscript (1648)
• Gunter Quadrant with Case (17th century)
• Mathematics for a Military Academy in Padua, by Valeriano Bonvicino (1665)
• ​Iamblichus the Chaldaean's Greek translation of the Introduction to Arithmetic of Nicomachus of Gerasa (1668 Latin translation)
• Giovanna Battista Nigroni's Manuscript on Area and Volume (1675)
• Jacques Buot’s Introduction aux Mathematiques (1675 or later)
• Dutch Surveying Manuscript, by Sebastianus David Louys (1681)
• Jan Coutereels's Cyffer-Boek (1690)
• François Le Gendre's L'Arithmetique en sa Perfection (1690, original 1657)
• Arithmetica Practica of Henrik Coets (1698)
• Analysis geometrica of Antonio Hugo Omerique (1698)
• Manuscript for a Reckoning Master (early 18th century)
• 18th Century German Geometria (early 18th century)
• William Braikenridge's Exercitatio geometrica (1733)
• Saunderson's Elements of Algebra (1740)
• Fortification and Artillery on Corfu (1749)
• Andrea Tacquet’s Elements of Geometry (1753 English ed., original 1654)
• Landen's Residual Analysis (1758)
• Karsten's Theoretical Mathematics (1760)
• L’Hospital’s Treatise on Conic Sections (1776)
• John Lodge Cowley's An Illustration and Mensuration of Solid Geometry (3rd ed., 1787), contributed by Sid Kolpas
• Jean Étienne Montucla's Histoire des Mathématiques (1799-1802)
• Ruffini's Theory of Equations (1799) 
• Nathaniel Bowditch's The New American Practical Navigator (1802)
• Silvestre-François Lacroix's Élémens d’Algèbre (14th ed., 1825)
• Cauchy's Leçons sur le Calcul Différentiel (1829)
• Jean-Étienne Montucla's Histoire des Recherches sur la Quadratur du Cercle (1831, original 1754)
• Augustin Cauchy's Manuscript on Solving Equations (1831)
• Manuel Ayala's Elementos de matematicas (Peru, 1832)
• An Elementary Treatise on Plane and Spherical Trigonometry, and on the Application of Algebra to Geometry; from the Mathematics of Lacroix and Bézout, trans. John Farrar, owned by Florian Cajori (3rd ed., 1833)
• Bulgarian Arithmetic (1833)
• Oliver Byrne's A Short Practical Treatise on Spherical Trigonometry (1835)
• Olinthus Gregory's Mathematics for the Practical Man (2nd American ed., 1836, original 1825)
• Sylvestre Lacroix's Essays on Teaching in General: and the Teaching of Mathematics in Particular (4th ed., 1838, original 1805)
• Cauchy's Mathematical Physics (1840)
• Victor Puiseux's Mathematical Papers (1842)
• Andrew Motte's translation of Principia Mathematica by Isaac Newton (1846 American ed., original 1729)
• De Morgan's Syllabus of a Proposed System of Logic (1860)
• Charles Dodgson's Trigonometric Symbols (1861)
• Isaac Todhunter's A History of the Progress of the Calculus of Variations During the Nineteenth Century (1861)
• William Stanley Jevon's Pure Logic or the Logic of Quality Apart from Quantity (1864)
• Felter’s Arithmetic for Children (1865)
• Euclid's Elements for China (1865)
• Collected Mathematical Works of Li Shanlan (1867)
• P.G. Tait's Elementary Treatise on Quaternions (1867)
• Whitworth's Choice and Chance (1870 2nd ed., original 1867)
• Todhunter's Differential Calculus (1871)
• Bernhard Riemann's Gesammelte Mathematische Werke (1876)
• William J. Milne's First Lessons in Arithmetic (1878)
• Notes on Lectures of Weierstrass (1879)
• Notes on Lectures of Poincare (1881-1883)
• Byerly’s Differential Calculus for Harvard Students (1888)
• Todhunter's Theory of Equations (1888)
• Karl Fink's Kurzer Abriss einer Geschichte der Elementar-Mathematik (Brief History of Elementary Mathematics) (1890)
• Lucas’s Theory of Numbers (1891)
• Peano's Vector Calculus (1891 German ed., Ital. orig. 1888)
• Bolyai’s Essay on Euclid’s 5th Postulate (1896, 1st ed. 1891, original 1832)
• Collected Works of Enrico Betti (1903)
• Augustus De Morgan's On the Study and Difficulties of Mathematics (1910 reprint, original 1831)
• Kaye's Indian Mathematics (1915)
• Dickson's History of the Theory of Numbers (1919)
• R. A. Fisher’s Statistics Books (1938)