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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!

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

Classroom-ready student project based on 11 lines of Sanskrit verse from the 6th-century text Pañcasiddhāntikā (The Five Canons) by Varahāmihira (505–587 CE).

Reprint of Dick Davitt's 2000 "The Evolutionary Character of Mathematics," originally published in the NCTM's Mathematics Teacher, with new commentary by Judith Grabiner.

The author uses 19th-century efforts to prove the converse of the Function Independence Theorem to show students that struggles and missteps in mathematics are normal.

A student project based on Ptolemy's computation of the length of gnomon shadows in the Almagest.

Provides an English translation of a paper written in 1726 by a 12-year-old Alexis Clairaut.

Reprint of Frank Swetz's 1977 "The 'Piling up of Squares' in Ancient China," originally published in the NCTM's Mathematics Teacher, with commentary and a brief bibliography covering 40 years of the history of Chinese mathematics (and its use in teaching) by Joel Haack.

A student-ready activity, ideal for pre-service elementary mathematics teachers.

An open-ended exploration of a (lesser-known) Babylonian tablet.

A recounting of the 18th century discovery of voting theory, and a student project based on the tale.

A mathematical exploration of congressional representation, from the 1790 US Census to the Huntington-Hill Method.

A project based on a work by Cantor that helps students bridge the gap from more familiar mathematics to the abstract concepts of topology.

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

PDF of the 2020 winning entry by Jeffrey Powers of Grand Rapids Community College.

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