Mathematics of Symmetry


Symmetry is found everywhere in nature, as well as in art, architecture, and design.
We see it in the left-right symmetry of our bodies and the bodies of many animals, but there is also the five-fold symmetry of a starfish. Symmetry is found in buildings and in beautiful paintings, such as in this work of M.C. Escher.



Understanding symmetry has been key to uncovering the fundamental laws of nature, and describing them in a systematic way. For example, modern particle physics would not exist without group theory, which is the study of symmetries.
Symmetry is one of the most powerful and important concepts in modern mathematics.
In this course, we will investigate mathematical objects and explore different ways of finding and describing symmetries of these objects. We will show how two symmetries may be combined to produce a third, and we will explore the patterns that result.
Students will learn to think of good questions and how to tackle them. Conceptual and analytical approach will be combined with hands-on activities and group discussions.


The teacher is Dr. Eli Lebow who did his undergraduate work at Harvard University in mathematics and physics, and his Ph.D. at Cal in mathematics. Among other places, he taught middle school students at the Academic Talent Development Program in Berkeley, and undergraduate students at UC Berkeley.


  • The class is for 8 – 11th grade students.
  • It is a 10 week long class that meets once a week for 1 hour.
  • Groups will meet on Tuesdays at 5:45 pm.
  • The cost is $200 for the semester.
  • Classes begin on Tuesday, October 6 and end on Tuesday, December 15th.


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