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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!

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

An introduction to Andean khipus, the knotted-string devices used for numerical and non-numerical recordkeeping, with pointers to online collections databases containing more information.

Razones para usar imágenes de libros y objetos históricos para motivar a los estudiantes dentro y fuera del aula de clases.

A student project based on Euler's discovery of a new technique for differential equations, and Johann Bernoulli's reaction to it.

Download the first- and second-place winning papers from the 2022 contest.

Reprint of Po-Hung Liu's 2003 "Do Teachers Need to Incorporate the History of Mathematics in Their Teaching?," originally published in the NCTM's Mathematics Teacher.

A student project based on the original writings of Georges-Louis LeClerc, the Comte de Buffon.

This article presents photographs of ancient Egyptian hieroglyphs that instructors can use when teaching numeration systems.

Reprint of Robert Reys' and Barbara Reys' 2011 "The High School Mathematics Curriculum—What Can We Learn from History?", originally published in the NCTM's Mathematics Teacher.

Resources for sharing Kepler's fascinating studies of the rhombic dodecahedron with students.

The rod numerals of ancient China are promoted as an alternative for teaching preservice teachers about numeration systems.

A student project based on Fourier's 1827 memoire: Théorie analytique de la chaleur.

The author shares some of the research surprises he encountered while writing Republic of Numbers (JHU Press, 2019).

Classroom-ready student project based on a 16th-century text by Regiomontanus.

A set of three mini-Primary Source Projects based on work by Gauss, for use in Calculus 2.