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Discussion Guide

Click here to download (.pdf, 1.5 mb)

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Secrets of the Surface (.pdf format)

Extra Features

The DVD and Blu-ray editions include six extra features.

  • Space of All Triangles Up to Similarity
    by Grant Sanderson (2:44)
    Grant Sanderson specializes in the animation of mathematical ideas accompanied by his own narration. Much of his work can be found at In Space of All Triangles Up to Similarity, he explains an important feature of Mirzakhani’s work.
  • Negative Curvature (2:58)
    The idea of negative curvature is key to understanding the shapes at the center of Mirzakhani’s work. This short piece illustrates the idea in several ways and includes explanations by Siavash Shahshahani and Alex Wright.
  • Pairs of Pants (1:43)
    Jayadev Athreya explains why this configuration of tori is commonly referred to as pairs of pants.
  • Pathological Foliations (1:36)
    Mathematician Amie Wilkinson has applied her interest in symmetry to fabric design. This short lyrical piece includes her explanation and a few examples of her fabrics.
  • Math in Iranian Architecture (5:14)
    Payam Seraji, founder of the Isfahan Mathematics House, discusses the use of mathematics by the artists and architects who created some of Isfahan’s most spectacular buildings, including the Jameh mosque. His words are illustrated with examples from those sites filmed in March 2019.
  • History of Math in Iran (13:10)
    A brief history of a vast subject bravely compressed by Hossein Masoumi Hamedani of the Iranian Institute of Philosophy and Omid Karamzadeh from the Math Department of Shahid Chamran University of Ahvaz. The accomplishments of the current generation of talented Iranian mathematicians exemplified by Maryam Mirzakhani are put in a wider historical context, showing Iran’s pivotal role in the preservation and transmission of mathematical ideas going back to ancient Greece, India, and other cultures.