MIT Massachusetts Institute of Technology

The Geometry of Parabolic Sand Dunes

Mohammad Zuheir Abu-Sbeih

Associate Professor of Mathematics

Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals (KFUPM)
Dharan, Saudi Arabia

*This video was sponsored by
Saudi Aramco and produced
by Sultan Bin Abdel Aziz
Science & Technology Center

One of the main problems facing Saudi Arabia and many other countries in the region is the movement of sand, which threatens the urban areas.  With the expansion of new installations and other projects, sand dune movement is costing governments a lot of money and energy. We shall shed some light on this problem and introduce students to some basic knowledge about this issue. This knowledge will include information related to dune movement, factors affecting their movement, the stabilization of dunes, and different types and shapes of dunes. We investigate a particular type of sand dunes, the barchan sand dune, and analyze its geometry and how to approximate its volume and what parameters are needed. For this lesson, students should have a solid exposure to both three-dimensional geometry and single variable calculus. The lesson could be completed in a 45-50-minute class period.

Dr. Abu-Sbeih is Professor of Mathematics at King Fahd University of Petroleum and Minerals. Currently he is the Undergraduate Coordinator in the Mathematics and Statistics Department. His interest is in the area of combinatorics and graph theory, especially in enumeration and embedding problems. He also has an interest in math education. He enjoys spreading the culture of mathematics in the society to benefit all. Read more about him at

This Wikipedia site provides definitions and descriptions of different sand dune types.

This Wikipedia site discusses the many aspects of sand dune stabilization.

This site, sponsored by SaharaSafaris, is a good general information site and also provides the Arabic names of the several dune types.

This site, sponsored by the U.S. Geologic Survey, defines and describes five basic types of dunes: crescentic, linear, star, dome, and parabolic. Satellite photos of each type are included.

This site, sponsored by Edumedia, presents an animation of the behavior of sand dunes.

This site, provided by the faculty of King Saud University, presents the abstract of a paper studying the control of the sand flow field around a specific dune, the Barchan Sand Dune

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This Lesson is in the following clusters: Geometry