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Convergence

A woman, the Muse of Geometry, instructs a group of stonemasons. Welcome to Convergence, MAA's online peer-reviewed journal where history, mathematics, and teaching meet! Since 2004, Convergence has offered a wealth of resources to help instructors enrich their students’ learning experiences by teaching 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

HOM SIGMAA 2023 Student Paper Contest Winner

Download the first-place winning paper from the 2023 contest.
Who? How? What? A Strategy for Using History to Teach Mathematics

Reprint of Patricia Wilson's and Jennifer Chauvot's 2000 "Who? How? What? A Strategy for Using History to Teach Mathematics," originally published in NCTM's Mathematics Teacher.
Historical Notes for the Calculus Classroom

Introduction to a series of short articles on the history of calculus, written for instructors.
A Mysterious Copy of Lacroix’s Traité Élémentaire de Calcul Différentiel et de Calcul Intégral: A Mathematical Treasure

Mystery surrounding an 1828 copy of Lacroix's textbook, signed by De Morgan—and intended for Sylvester??
Aiding the Teaching of Geometry and Affording Mathematical Recreation: Paper Folding in the Spirit of Sundara Rao of Madras

A history of paper folding in mathematics education, emphasizing the role of Sundara Rao’s 1893 Geometrical Exercises in Paper Folding.
Fermat’s Method for Finding Maxima and Minima: A Mini-Primary Source Project for Calculus 1 Students

A classroom-ready project on optimization, based on excerpts from Fermat's original work.
Historically Speaking

Reprints from the "Historically Speaking" column of Mathematics Teacher.
Quotations in Context

A series of columns, first published in the CSHPM Bulletin, that considers why oft-repeated quotations about mathematics were originally published and places them in their original context.
HoM Toolbox, or Historiography and Methodology for Mathematicians

Historiography and methodology for students and instructors interested in pursuing scholarship in the history of mathematics.
Fourier’s Infinite Series Proof of the Irrationality of e: A Mini-Primary Source Project for Calculus 2 Students

A student project for Calculus 2 based on Fourier's original proof of the irrationality of \(e\).
Keys to Mathematical Treasure Chests: Andean Khipus

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.
El Gabinete de Maravillas Matemáticas de Pantas: Imágenes e Historia de las Matemáticas

Razones para usar imágenes de libros y objetos históricos para motivar a los estudiantes dentro y fuera del aula de clases.
Solving Linear Higher Order Differential Equations with Euler and Johann Bernoulli: A Mini-Primary Source Project for Differential Equations Students

A student project based on Euler's discovery of a new technique for differential equations, and Johann Bernoulli's reaction to it.
HOM SIGMAA 2022 Student Paper Contest Winners

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