A World from a Sheet of Paper

Talk by Tadashi Tokieda: https://www.youtube.com/watch?v=8p02DtmyQhU

• The creases in a folded paper are not random. They satisfy some properties:
  • The number of lines meeting at a point is even

  • The sum of angles must be equal to 360 degrees

    \(\sum_i \alpha_i = 360\)

  • The alternating sum of angles must of zero.

    \(\sum_i (-1)^i \alpha_i = 0\)

• Poisson's Ratio for isotropic material lies between -1 to 1/2
• Miura Ori is used for folding satellite solar panels, antennas, and you can use it to fold maps!.
• A randomly crumbled paper has a negative Poisson's ratio.
• Paper lies in 2.5D.