Students can benefit from exploring original sources in mathematics, and the ancient Śulba-sūtras texts from India are a great source of applications of mathematics, especially geometry. These instructions for building fire altars using ropes include constructions of squares and rectangles, along with transformations of one shape to another with the same area. Using GeoGebra applets and hands-on activities, students can explore some mathematical contributions from ancient India, and strengthen their own geometric reasoning. For more of a challenge, students can prove that the instructions are correct, resulting in the desired shape.
Figure 5. Model of a falcon fire altar from an Athirathram ceremony in 2011. (Photo from Wikimedia Commons attributed to Arayilpdas at Malayalam Wikipedia.)
Common Core State Standards Initiative: http://www.corestandards.org/
[Datta] Datta, Bibhutibhusan. The Science of the Sulbas: A Study in Early Hindu Geometry. Calcutta University Press, 1932.
GeoGebra: http://www.geogebra.org
[Huffman and Thuong] Huffman, Cynthia J. and Scott V. Thuong, "Ancient Indian Rope Geometry in the Classroom," Convergence (October 2015), DOI:10.4169/convergence20151001: https://www.maa.org/press/periodicals/convergence/ancient-indian-rope-geometry-in-the-classroom-mathematics-in-ancient-india
[Plofker1] Plofker, Kim. Mathematics in India. Chapter 4 in Katz, Victor, editor. The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press, 2007, pp. 385-514.
[Plofker2] Plofker, Kim. Mathematics in India. Princeton University Press, 2009.
[Prasoon] Prasoon, Shrikant. Indian Scriptures. Pustak Mahal, 2010, Ch. 2.
[Sen & Bag] Sen, S.N., and A.K. Bag. The Śulbasūtras. Indian National Science Academy, 1983.
The authors are indebted to the editor and anonymous referees for help in improving the article. Thank you to Dr. Janet Beery for suggesting we take a look at Indian rope geometry in the first place.
Cynthia J. Huffman is a University Professor in the Department of Mathematics at Pittsburg State University. She has always been interested in history of mathematics but her interest was especially sparked by participation in several of the MAA Study Tours. Her research areas include computational commutative algebra and history of mathematics. Dr. Huffman is a handbell soloist and has a black belt in Chinese Kenpo karate. | |
Scott V. Thuong is an Assistant Professor in the Department of Mathematics at Pittsburg State University. His research areas include topology, geometry, and the history of mathematics. In his spare time, Dr. Thuong enjoys a good game of badminton, table tennis, or tennis. |