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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

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

The functional approach of circle trigonometry is the historical approach!

Two problems that endured across time, place, and culture

Influence of culture on mathematical interests of Catholic, Jewish, and Islamic scholars

Read Proclus; explore gnomons.

Classroom project in which students see how mathematicians shape definitions over time

Contributions of Euler, Gauss, and Sylvester to the development of the number-theoretic totient or phi-function

Word problems, square roots, and pi from the 1321 'Maaseh Hoshev' or 'Art of the Calculator'

Motivation for the study of analysis

A compendium of determinant theory & a salvo for the analytic approach

Mathematics, culture, and community outreach for liberal arts students

Obtain the formulas as Euler did: using differentials.

... for one- or two-day use in class

... featuring the arithmetic of fractions as you've (possibly) never seen it before!