In mathematics, Maekawa's theorem is a theorem used in the mathematics of paper folding. It basically involves flat-foldable origami crease patterns that are determined by a variation of valley-creases and mountain-creases. Maekawa's theorem states that the numbers of mountain folds and valleys always differ by two at every vertex—no matter the direction.
Mathematics of setting cubes
Mathematics of folding paper
Mathematics of wave movement
Mathematics of scalar surfaces
An odd number
A decimal number
An even number
Half of the angle
S. Murata
B. Jurtala
Jan Nelson
Robert Oneil
It does not completely characterize the flat-foldable vertices
It shows only the angles of the vertical cortex
It is only applicable to folds greater than 180 degrees
The theorem is mutually exclusive to angles of a straight shape
The number of mountain folds is the same in either direction
The number of valley and mountain folds is always the same in either direction
The numbers of valley and mountain folds always differ by two in either direction
The number of valley fold is the same in both directions of the vertex
It is not possible to color the regions of the creases
It is always possible to color the regions between the creases with two colors, such that each crease separates regions of differing colors
Each crease seperates the regions into 5 different colours
It is not possible to color the region creases with two colors but each crease can still be separated to regions of differing colors
Origami Theorem
Kawasaki Theorem
Murata Theorem
Vannelson Theorem
Jacques Justin
Hull Thomas
Takahama Inoshi
Craig Edwards
Theorem of Wide Angles
Viva Origami
Theories of Origami Design
Mathematical Modeling Based on Origami Design
Angle wideness of origami models
Crease regions in origami models
Fold number in origami models
Flat-foldability of origami models