Tetrahedra: From Aristotle’s Mistake to Unsolved Problems

  • Speaker
  • Bjorn Poonen, Ph.D.Massachusetts Institute of Technology
Date & Time


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Tetrahedra are three-dimensional shapes with four triangular faces. Which tetrahedra can tile to fill a three-dimensional space? Which tetrahedra have rational dihedral angles (the angle between two intersecting planes)? Which tetrahedra can be sliced and reassembled into a cube? Each of these three problems has been around for at least 45 years, and one of them is over 2300 years old. In this lecture, Bjorn Poonen will discuss the status of these problems and explain how he solved one of them in collaboration with K. Kedlaya, A. Kolpakov, and M. Rubinstein.

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About the Speaker

Poonen researches number theory and algebraic geometry at MIT. He has received the Guggenheim, Packard, Rosenbaum, Simons, and Sloan Fellowships, as well as the Chauvenet Prize, a Miller Professorship, and the MIT School of Science Prize in Undergraduate Teaching. He is a Simons Investigator, Fellow of the American Academy of Arts and Sciences, and founding managing editor of Algebra & Number Theory. Twenty-five mathematicians have earned a Ph.D. under his supervision. 

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