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Convergence

Welcome to Convergence! This MAA publication offers a wealth of resources to help you teach mathematics using its history.

Make Convergence your source for math history and its use in teaching!

Dummy View - NOT TO BE DELETED

Mathematical Treasures

  • Completing the square in a manuscript copy of Al-Khwarizmi's 9th century algebra text

  • Finding heights in Galileo's Geometrical Compass (1640)

  • Title page of Galileo's Geometrical Compass (1640)

  • Spiral from Albrecht Durer's geometry book (1538)

  • Ellipse from Albrecht Durer's geometry book (1538)

  • Title page of Cardano's Ars Magna (1545)

  • From a 1650 copy of the 12th century Lilavati of Bhaskara II

  • Title page of Simon Jacob's Rechenbuch (1565 edition)

  • Finger counting in Luca Pacioli's Summa de arithmetica (1494)

  • "Allegory of Arithmetic" from Gregor Reisch's Margarita Philosophica (1503)

  • English tally stick from 1296 is marked William de Costello, Sheriff of London.

  • This large English tally stick was used as a receipt.

  • Notched wooden English tally sticks served as receipts.

  • German brass protractor with Baroque decoration from about 1700
     

  • Nested Austrian weights are elaborately decorated and marked 1787.

  • This Italian astrolabe was constructed by Bernard Sabeus of Padua in 1558.

  • Da Vinci's stellated dodecahedron in Pacioli's Divina proportione (1509)

  • Completing the square in a manuscript copy of Al-Khwarizmi's 9th century algebra text

  • Thomas Digges used a quadrant to measure the height of a tower in his Pantometria (1571).

  • Peter Apian's A Geographical Introduction (1534) applied geometry and trigonometry.

  • Peter Apian's device for computing sines in his Instrumentum sinuum (1534)

  • Peacock and snake problem from 1650 copy of the 12th century Lilavati of Bhaskara II

  • Kepler's sketch of the apparent retrograde motion of Mars in Astronomia Nova (1609)

  • Kepler compared planetary motion per Ptolemy, Copernicus, Brahe in Astronomia Nova (1609).

  • Title page of Johannes Kepler's Astronomia Nova (1609) based on Brahe's data

  • Notched wooden tally sticks used to record financial transactions in England (1296)

  • Late 19th century Korean wooden computing rods or sangi

  • This 15th century Italian compass and ruler converted Roman units to other units in use at the time.

  • Italian armillary sphere (1550): mechanical model of universe showing circular orbits of planets

Featured Items

Teaching and Learning the Trigonometric Functions through Their Origins: Episode 2 - Hipparchus’ Table of Chords

Second episode in the series, Teaching and Learning the Trigonometric Functions through Their Origins; deals with construction of a table of chords.
Topology from Analysis: A Mini-Primary Source Project for Topology Students

A project based on a work by Cantor that helps students bridge the gap from more familiar mathematics to the abstract concepts of topology
Pathways from the Past: Classroom-Ready Materials for Using History to Teach Mathematics

A collection of reproducible student activity sheets that use historical settings to teach or reinforce basic mathematical lessons

 
HOM SIGMAA 2020 Student Paper Contest Winner

PDF of the 2020 winning entry by Jeffrey Powers of Grand Rapids Community College
Braess’ Paradox in City Planning: A Mini-Primary Source Project for Multivariable Calculus Students

A student project in multivariable optimization based on a classic paper in transportation science

 
Word Histories: Melding Mathematics and Meanings

The origins of some common mathematical words that can enrich student learning
Teaching and Learning the Trigonometric Functions through Their Origins

A series of curricular units based on primary source texts for use in teaching and learning trigonometry
Mabel Sykes: A Life Untold and an Architectural Geometry Book Rediscovered

An incredible compendium of geometry problems, illustrated with Geogebra applets, by a little-known author
Investigations Into d'Alembert's Definition of Limit: A Mini-Primary Source Project for Students of Real Analysis and Calculus 2

A project for today's students based on d'Alembert's 1754 definition of a limit.
Why History of Mathematics?

Reprint of Glen Van Brummelen's article, Why History of Mathematics? from the Fall 2019 issue of BCAMT Vector.
A Mathematical History Tour: Reflections on a Study Abroad Program

A unique course combining the history of mathematics and travel.
Correspondence from Mathematicians

A classroom research project that helps students discover the origins of familiar mathematical concepts
Regression to the Mean: A Mini-Primary Source Project for Statistics Students

A student project based on Galton's statistical paper "Regression to the Mediocrity in Hereditary Stature"

 
An Explication of the Antilogism in Christine Ladd-Franklin's "Algebra of Logic"

An overview of Ladd-Franklin's contributions to symbolic logic, based on an explication of an excerpt from her doctoral dissertation.