Paper Folding

Paper Folding
Origami is an ancient Chinese and Japanese art of paper folding.This was the first usage of the word "origami" so far traced in Japan. The word "origami" came to be used occasionally for another kind of ceremonial folding, namely for "tsutsumi", or formal wrappers, by the beginning of the 18th century. However, its use for recreational origami of the kind with which we are familiar did not come until the end of the nineteenth century or the beginning of the twentieth. Before that, paperfolding for play was known by a variety of names, including "orikata", "orisue", "orimono", "tatamgami" and others.In the geometry of paper folding, a straight line becomes a crease or a fold. Instead of drawing straight lines, one folds a piece of paper and flattens the crease. Folding paper is analogous to mirroring one half of a plane in a crease. Thus folding means both drawing a crease and mapping one half of a plane onto another. As in the usual Geometry, the distinction is being made between experimentation with the physical paper and the abstract theory of "paper folding". "Abstract paper" may be folded indefinitely although in practice the number of folds is by necessity limited.
The most well-known construction is "straight edge and compass" construction, which refers to the geometric operations that can be formed with only those two instruments (note that the straight edge is not a ruler with length markings). It is well-known that SE&C constructions can be encompassed (no pun intended) by four basic axioms, first defined by Euclid, over 2000 years ago. It is also well known that there are certain operations that are impossible given just a straight edge and compass.