The folding sequence of origami includes the use of geometry, and for complex models, knowledge on Maths. There are also some facts that people in the past have discovered about origami (please do note that the following statements only applies to models without curved creases and pinch creases):
1) If you make a squash or reverse fold, or fold more than a layer at once in the same direction together, and unfold it completely (you get back to a square), you will find that the difference between the number of valley and mountain folds is always two. No matter how complex or simple the model is, as long as you did at least either one of the three stated before, the model's Crease Pattern will have two more mountain or valley folds than the other.
2) If you add up all the angles of a Crease Pattern, the sum is always a multiple of 180.
3) A piece of square paper has four sides. All the lines are from one side of the square to another side of the square. They do not stop halfway. However, a valley crease could stop halfway and get replaced by a mountain crease. This, too, applies to other shapes.
One of Robert Lang's origami lectures he gave at a TED conference is available online at http://www.ted.com/index.php/talks/robert_lang_folds_way_new_origami.html.
1) If you make a squash or reverse fold, or fold more than a layer at once in the same direction together, and unfold it completely (you get back to a square), you will find that the difference between the number of valley and mountain folds is always two. No matter how complex or simple the model is, as long as you did at least either one of the three stated before, the model's Crease Pattern will have two more mountain or valley folds than the other.
2) If you add up all the angles of a Crease Pattern, the sum is always a multiple of 180.
3) A piece of square paper has four sides. All the lines are from one side of the square to another side of the square. They do not stop halfway. However, a valley crease could stop halfway and get replaced by a mountain crease. This, too, applies to other shapes.
One of Robert Lang's origami lectures he gave at a TED conference is available online at http://www.ted.com/index.php/talks/robert_lang_folds_way_new_origami.html.
