Selected Topics in Mathematics - Online Edition: Talk 02 (Igor Pak)

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A talk by Professor Igor Pak (UCLA),

Title: Domes over curves

Abstract: A closed PL-curve is called integral if it is comprised of unit intervals. Kenyon's problem asks whether for every integral curve γ in R3, there is a dome over γ, i.e. whether γ is a boundary of a polyhedral surface whose faces are equilateral triangles with unit edge lengths.

First, we give an algebraic necessary condition when γ is a quadrilateral, thus giving a negative solution to Kenyon's problem in full generality. We then prove that domes exist over a dense set of integral curves. Finally, we give an explicit construction of domes over all regular n-gons.

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  • Added:20 Feb 2021
  • Uploaded by:Matty Van-Son
  • Length:53:17
  • Views:23
  • Comments:0

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