What's in Convergence? - Contents of Volume 13 - 2016

Editor:  Janet Beery

Associate Editors: Amy Ackerberg-Hastings, Janet Heine Barnett, Kathleen Clark, Lawrence D'Antonio, Douglas Ensley, Victor Katz, Daniel Otero, Gabriela Sanchis, Randy Schwartz, Lee Stemkoski, Gary Stoudt

Founding Editors: Victor Katz, Frank Swetz

Articles

President James A. Garfield's Proof of the Pythagorean Theorem, by Sid Kolpas

Garfield's 1876 proof, plus a memorial visiting card featuring a photograph of Garfield (1831–1881).

Descartes' Method for Constructing Roots of Polynomials with 'Simple' Curves, by Gary Rubinstein

Descartes' methods from his 1637 'Geometry' explicated and illustrated using interactive applets.

Letter and Visiting Card of Augustus De Morgan, by Sid Kolpas

Visiting card with photograph (circa 1866), brief biography, student sketch (1865), An Essay on Probabilities (1838), and letter to Indologist H. H. Wilson (1843).

When Was Pierre de Fermat Born?, by Friedrich Katscher

An argument that Pierre de Fermat was born in 1607 rather than in 1601.

The Duplicators: Eutocius's Collection of Cube Duplications, by Colin B. P. McKinney

Solutions by ancient Greek mathematicians of the classical duplicating the cube problem – with extra tools allowed! – featuring translations from the Greek and interactive applets.

Archimedes' Method for Computing Areas and Volumes, by Gabriela R. Sanchis

Archimedes' use of the Law of the Lever to compute areas and volumes in The Method, with classroom-ready examples, exercises, and interactive applets.

HOM SIGMAA 2016 Student Paper Contest Winners

Download the two winning papers from the 13th annual competition, "A Latent Element of Alice's Agency in Wonderland: Conservative Victorian Mathematics" and "The Evolution of the Circle Method in Additive Prime Number Theory."

Al-Maghribî’s Mecca Problem Meets Sudoku, by Ilhan M. Izmirli

Solutions to an early 17th century puzzle from Istanbul can be generated from solutions to modern day Sudoku puzzles.

Johannes Scheubel's 1551 Algebrae Compendiosa, by Sid Kolpas

Selected examples for classroom use feature early algebraic notation and methods.

Misseri-Calendar: A Calendar Embedded in Icelandic Nature, Society, and Culture, by Kristín Bjarnadóttir

History of this two-season calendar from Viking times to today, with animations and ideas for your classroom.

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 2016:

• Three Old Babylonian Tablets (1990-1700 BCE)

• Tomb of Menna (1420–1411 BCE)

• Archimedes on Curved Surfaces (1350-1372, original: 3rd century BCE)

• Carmen de Algorism (c. 1240)

• Al-Tusi's Euclid's Elements (13th century)

• Geometry Treatise from Islamic Spain (13th century)

• Manual of Islamic Inheritance Law (13th century)

• Anonymous Practica geometriae (13th century)

• De triangulis of Jordanus de Nemore (14th century or later copy of 13th century manuscript)

• Zhu Shijie's New Arithmetic Enlightenment (1299)

• Richard Swineshead's Opus aureum calculationum (1477, original ca 1350)

• Peuerbach's and Regiomontanus' Ptolemy (1496)

• Alberti's Methods for Measuring Heights (15th century)

• The Arithmetic of Grammateus (1518)

• Royal Presentation Manuscript of Le Sphere du Monde (1549)

• Johannes Scheubel's Algebrae Compendiosa (1551), contributed by Sid Kolpas

• Frederico Commandino's Complete Works of Archimedes (1558)

• Pietro Cataneo's Practice of Two Primary Mathematics (1559)

• Adrian Metius's Arithmetica et Geometriae (1626)

• Pierre de Savonne's 'Arithmetique (1630)

• Galileo's Two New Sciences (1638)

• Johannes Wilhelm Lauremberg's Gromaticae Liber Tres (1640)

• Evangelista Torricelli's Opera geometrica (1644)

• Van Schooten's De organica conicarum sectionum (1646)

• John Pell's Controversy with Longomontanus concerning the Quadrature of the Circle (1647)

• History of Mathematics of Vossius (1650)

• Frans van Schooten's Exercitationum Mathematicarum (1657)

• Adriaan Vlacq's Tabellen der Sinuum, Tangentium, und Secantium (1663, original 1636)

• Rene Descartes, Lettres (1663)

• Gottfried Wilhelm Leibniz's Dissertation de Arte Combinatoria (1666)

• Letter on Quadrature from Leibniz to Huygens (1674, published 1859)

• Jean Prestet's Elemens de mathématiques (1675)

• Mathematics and Architecture (1676)

• Illustrations of the 'System of the World' (1680)

• Theodoric Luders's Traicté Mathematique (1680)

• John Collins' Letter on 'Defects in Algebra' (reprinted in 1684)

• John Wallis's Treatise on Algebra (1685)

• Taylor's Treasury of Mathematicks (1687)

• Annual Report of the French Academy of Sciences (1693)

• Erhard Weigel's Philosophia Mathematica (1693)

• Jacques Ozanam's Cours de mathématique (1693)

• Opera mathematica of John Wallis (1693-1699)

• John Wallis's Collected Works (volume 1, 1695)

• Thomas Fanlet deLagny's New Elements of Arithmetic and Algebra (1697)

• Christian Schessler's Demonstrationes mathematic oder Untersuchung derer mathematischen warheit und unwarheiten (1698)

• Arbuthnot’s Essay on Usefulness of Mathematics (1745, original 1701)

• David Gregory's Commentary on Euclid (1703)

• Andrea Tacquet's Practical and Theoretical Arithmetic (1704, original 1656) and Elementa geometricae (1752, original 1654)

• Halley's Conics of Apollonius (1710)

• Christian Wolff's Foundations of Mathematics (1710/1772)

• Jacques Ozanam's A Complete Course of the Mathematicks (translated 1712)

• Evangelista Torricelli's Academic Lectures (1715)

• Christian Wolff's Mathematical Lexicon (1716)

• Malcolm's Arithmetick and Book-keeping (1718)

• Edward Hatton's Mathematical Manual (1728)

• Malcolm's New System of Arithmetick (1730)

• John Lowthorp, ed., The Philosophical Transactions and Collections, to the Year 1700 (1731 edition)

• John Ward's Young Mathematician's Guide (1734, original 1703)

• Berkeley's Defence of Free-Thinking (1735)

• Spanish Commerical Arithmetic (1736)

• John Saxton's The Merchant's Companion (1737)

• Correspondence between Leibniz and Johannes Bernoulli (1745)

• Mayer's Mathematischer Atlas (1745)

• Abraham de Moivre's Annuities on Lives (1725)

• Darjes' Ground of all Mathematics (1757)

• Joseph Fenn's New and Complete System of Algebra (1767)

• Thomas Simpson's Doctrine of Annuities and Reversions (1775)

• Georg Vega's Logarithmic Tables (1783)

• Georg Vega's Lectures on Mathematics (1784)

• Waring's Meditationes Analyticae (1785, original 1773)

• Francis Maseres's Doctrine of Permutations (1795)

• 18th Century U.S. College Mathematics

• Webber's Mathematics for Harvard Students (1808, original 1801)

• Thomas Jefferson's Octagon (18th–19th centuries)

• Bussot's General History of Mathematics (1803)

• Pierre Simon de Laplace, mathematics curriculum in Journal de L’Ecole Polytechnique (1812)

• John Bonnycastle's Arithmetic (1815, original 1780) and Algebra (1811, original 1782)

• Hutton's Tracts on Mathematical Subjects (1812)

• Hutton’s Philosophical and Mathematical Dictionary (1815)

• Etienne Bézout's First Principles of the Differential and Integral Calculus, translated by John Farrar and George Barrell Emerson (1824, 1764-1767 original)

• August Ferdinand Mobius' Der Barycentrische Calcul (1827)

• Augustus De Morgan's Elements of Arithmetic (1858, original 1830)

• Augustus De Morgan's Elementary Illustrations of the Differential and Integral Calculus (1899, original 1832)

• Augustus De Morgan's Elements of Algebra (1835)

• The Calculus of Elias Loomis (1858, original 1835)

• Cambridge Problems 1801-1820 (1836)

• De Morgan's Essay on Probabilities and their Application to Life Contingencies and Insurance Offices (1838) 

• Abel's Complete Works (1839)

• Cambridge Miscellany of Mathematics (1842)

• Augustus De Morgan's Differential and Integral Calculus (1842)

• Letter and Visiting Card of Augustus De Morgan, contributed by Sid Kolpas

  • Letter about Indian astronomer Varāhamihira (1843)
  • De Morgan's An Essay on Probabilities (1838)
  • Student's drawing of De Morgan (1865)
  • Visiting card with photograph (c. 1866)

• Carl Jacobi's Opuscula mathematica (1846)

• Euler’s Commentationes Arithmeticae (1849)

• Brugsch on Ancient Egyptian Numbers (1849)

• De Morgan's Trigonometry and Double Algebra (1849)

• Charles Davies's The Logic and Utility of Mathematics (1869, original 1850)

• H. C. Schwarz's Philosophy of Mathematics (1853)

• A New Mathematics Curriculum for China (1853/1859)

• Boole's Investigation of the Laws of Thought (1854)

• George Hale Puckle's An Elementary Treatise on Conic Sections and Algebraic Geometry (1854)

• Comte's Philosophy of Mathematics (1855)

• George Biddell Airy on Theory of Observational Error (1861)

• Woepcke on Indo-Arabic Numbers (1863)

• Mathematical Papers of George Green (1871)

• Augustus De Morgan's Budget of Paradoxes (1872) (posted 12/21/16)

• Hankel's History of Mathematics (1874)

• Briot and Bouquet's Leçons de Géometrie Analytic (1875)

• Clebsch's Vorlesungen über geometrie (3 images) (1876)

• First Scandinavian Mathematics Journal (1876)

• James A. Garfield's Proof of the Pythagorean Theorem (1876), contributed by Sid Kolpas

• American Journal of Mathematics (1878)

• Jullien Models for Descriptive Geometry (ca 1880), contributed by Amy Shell-Gellasch

• Moritz Cantor's History of Mathematics (1880-1908)

• Complete Works of Augustin Cauchy, Vol. V (1885)

• Darboux's Theory of Surfaces (1887)

• Tannery's Oeuvres de Fermat, Vol. I (1891)

• Zeuthen's History of Mathematics (1896, original 1893)

• Collected Works of Tchebychef (Chebyshev, 1899)

• Gibbs' and Wilson's Vector Analysis (1901)

• Poincaré's Science and Hypothesis (1902)

• The Principia Mathematica of Russell and Whitehead (1910-1913)

• F. G. Hill's Development of Arabic Numerals in Europe (1915)

• Cajori's History of Limits and Fluxions (1919)

• Peirce’s Mathematical and Physical Papers (1926)

• Model of Elongated Pentagonal Pyramid (mid-20th century), contributed by Peggy Kidwell

• Hewlett-Packard HP28S Handheld Electronic Calculator from the AMS Centennial Meeting (1988), contributed by Peggy Kidwell

Reviews

Review of Mathematics in Ancient Egypt: A Contextual History, by Annette Imhausen. Reviewed by Frank J. Swetz.

Our reviewer finds the book to be "well written" and "well researched," and is grateful to the author for summarizing scholarship to date.

Review of Elements of Mathematics: From Euclid to Gödel, by John Stillwell. Reviewed by Frank J. Swetz.

Our reviewer concludes: "If you want to teach mathematics with its history, this is a way to do it!"