Need the Area of a Triangle? The Pope Can Help! – Conclusion, Resources, References, About the Author

Betty Mayfield (Hood College)



For many in the mathematics community, Gerbert’s 999 letter to Adalbold is their introduction to Gerbert and to his interest in mathematics. And for most of them, the introduction stops there. In this article we have been able to get a glimpse of Gerbert’s growth in his knowledge of computing the area of a triangle, from the rabbit-out-of-the-hat approach he taught his students, to his graphical explanation of the arithmetical rule and its faults, and finally to using insight gleaned from that graphical approach to find a better approximation for the altitude of a triangle. He deserves to be remembered as a creative and deep thinker as well as an accomplished teacher of mathematics.


Other entries about Gerbert and his work in this journal:

Mayfield, B. 2010, August. Gerbert d’Aurillac and the March of Spain: A Convergence of Cultures. Convergence.

The importance of Gerbert’s three-year stay in Catalonia to the development of his mathematical knowledge.

Swetz, F.J. 2019, January. Mathematical Treasure: Gerbert's Geometry. Convergence.

Images from a 12th-century copy of the Isagoge Geometriae, plus part of Gerbert’s letter to Adalbold. Provided courtesy of the University of Pennsylvania Libraries, The Lawrence J. Schoenberg Collection of Late and Early Renaissance Manuscripts, Kislak Center for Special Collections, Rare Books and Manuscripts.

Swetz, F.J. 2020, January. Mathematical Treasure: Mathematics of Gerbert of Aurillac.

Images from a French manuscript of the 12th century on geometry and astronomy, including the use of an astrolabe, and a 13th-century English manuscript illustrating the problem of determining the height of a remote tower using methods based on Gerbert’s geometry. Provided courtesy of The British Library.


Bubnov, N., ed. 1899. Gerberti Opera Mathematica (972–1003). Berlin: R. Friedländer und Sohn.

Cajori, F. 1922. Discussions: The Formula 1/2 a(a+1) for the Area of an Equilateral Triangle. American Mathematical Monthly 29(8): 303–307.

Darlington, O. 1947. Gerbert, the Teacher. The American Historical Review 52(3): 456–476.

Fitzpatrick, R., trans. and ed. 2008. Euclid’s Elements of Geometry.

Folkerts, M., and B. Hughes. 2016. The Latin Mathematics of Medieval Europe. In V. Katz, ed., Sourcebook in the Mathematics of Medieval Europe and North Africa, 4–223. Princeton: Princeton University Press.

Høyrup, J. 2014. Mathematics Education in the European Middle Ages. In G. Schubring and A. Karp, eds., Handbook on the History of Mathematics Education, 109–124. New York: Springer.

Lattin, H.P. 1961. The Letters of Gerbert: With His Papal Privileges as Sylvester II. New York: Columbia University Press.

Menninger, K. 1969. Number Words and Number Symbols: A Cultural History of Numbers (English translation). Cambridge, MA: The MIT Press.

Miller, G.A. 1921. The Formula 1/2 a(a+1) for the Area of an Equilateral Triangle. American Mathematical Monthly 28(6/7): 256–258.

Olleris, A., ed. 1867. Oeuvres de Gerbert, Pape sous le nom de Sylvestre II. Clermont: F. Thibaud.

About the Author

Betty Mayfield is Professor Emerita of Mathematics at Hood College in Frederick, Maryland, where she loved learning and teaching about the history of mathematics.