The Geometry of Paper Folding
Origami is fundamentally a study of applied geometry. While most people think of origami in terms of 'folds,' mathematicians view it as the division of a 2D plane. When you fold a square of paper into a complex base (like a Bird Base or a Frog Base), you are effectively 'consuming' the area of the paper to create the 'flaps' that will become the head, wings, or legs of the model.
Understanding Scale Reduction
As a model becomes more complex, the finished size becomes significantly smaller than the starting square.
- Crane (Bird Base): A 6-inch square will result in a finished bird with a wingspan of approximately 4.5 inches, but a body height of only 2 inches.
- Complex Models: High-level origami (like an insect with 6 legs and 2 antennae) might use a 20-inch square of paper to produce a finished model only 3 inches long.
Proportions of the Square
This calculator provides the dimensions of the internal 'modules' created by common origami bases.
Base Side = Starting Square * Proportion Constant
Paper Thickness and the 'Fold Limit'
The math of origami often ignores the thickness of the paper, but in the real world, it is the limiting factor. Every time you fold paper in half, the thickness doubles. After 7 folds, you are dealing with 128 layers of paper. For complex models, you must use extremely thin papers like 'Tissue Foil' or 'Washi' to avoid the corners becoming so bulky they tear.