If one looks inside a flat origami without unfolding it, one sees a zigzagged profile, determined by an alternation of "mountain-creases" and "valley-creases." The numbers of mountains and valleys always differ by 2.
Maekawa's Theorem
See also
Flat Origami, Kawasaki's Theorem, OrigamiThis entry contributed by Margherita Barile
Explore with Wolfram|Alpha
References
Demaine, E. D. "Folding and Unfolding." PhD thesis. Waterloo, Ontario, Canada: University of Waterloo, p. 26, 2001. https://uwspace.uwaterloo.ca/handle/10012/1068.Hull, T. "Notes on Flat Folding." http://web.merrimack.edu/~thull/combgeom/flatfold/flat.html.Kasahara, K. and Takahama, T. Origami for the Connoisseur. Tokyo: Japan Publications, 1987.Referenced on Wolfram|Alpha
Maekawa's TheoremCite this as:
Weisstein, Eric W., with contributions by Margherita Barile. "Maekawa's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MaekawasTheorem.html