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
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References
Demaine, E. D. Folding and Unfolding. Doctoral Thesis, University of Waterloo, Canada, p. 26, 2001. http://etd.uwaterloo.ca/etd/eddemaine2001.pdf.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:
Barile, Margherita. "Maekawa's Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/MaekawasTheorem.html