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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

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

 

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

Student activities that combine data collection with astronomical measurement methods due to Eratosthenes, Ptolemy and Galileo

A student project for beginning algebra, based on a source by al-Khwārizmī

A look at systems for representing and manipulating logical ideas developed in the 19th and 20th centuries

Our third puzzle by a math professor and a professional puzzle-maker!

A case where not simplifying fractions explains a curious rule for computing cube roots from medieval Arabic mathematics, with student exercises.

A classroom project based on Euler's 1740 solution of the Basel Problem

Recognition of Convergence's former editors, and a brief history of the journal.

Essay on the justifications for using history to teach mathematics.

An English translation of and readers' guide to a paper related to an debate on numerical integration.

Winning paper from 2019's HOMSIGMAA student contest.

A student project based on a paper by John Henry Smith about integration and nowhere dense sets

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.