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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

A series of articles introducing online collections documenting specific categories of mathematical objects, available for research and teaching.

A student project based on excerpts from letters between d'Alembert and Euler concerning the value of the logarithm of -1.

Biography of Sir Charles Scarburgh (ca 1615–1694) and discussion of his contributions to the history of mathematics.

A student project that explores the process of approximating a transcendental function by an algebraic one via mathematical results from medieval India.

PDF of the 2021 winning entry by Megan Ferguson of Adelphi University.

English translation of Mark Kac's first publication on a new derivation of Cardano’s formula, written while still in high school.

Mathematical mysteries of Rapa Nui (Easter Island) and related classroom activities, based on archeological findings from a recent field trip.

Discussion of a new tool for searching the contents of the British publication, Educational Times, with suggested uses for educators and researchers.

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.

A look at evolving calculus symbols for representing change.

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.