The name says fold and paper
Origami joins two Japanese words, oru, to fold, and kami, paper. PAPER itself was invented in China, and paper folding grew up in JAPAN once paper became cheap enough to use for something other than writing — first for ceremonial wrappings and gifts, and later as a pastime. Traditional origami uses a single SQUARE SHEET, no cuts and no glue.
Folding also developed separately in Europe; the paper BOAT and the salt-cellar fortune teller were being folded long before the Japanese word was known in English. What turned origami into a worldwide hobby was a way of writing folds down.
A language of dashes and arrows
In the 1950s the Japanese folder Akira Yoshizawa, who designed tens of thousands of MODEL figures in his lifetime, worked out a system of symbols for instructions: a line of dashes for a valley fold, a line of dots and dashes for a mountain fold, and arrows to show which way the paper moves. It is still the standard, so a DIAGRAM printed in Japan can be followed by someone who reads no Japanese.
Every CREASE counts. Folders line up each CORNER exactly and run a thumbnail along the fold to make it SHARP, because a small error early on becomes a large one after many LAYERS are stacked. Many models rely on SYMMETRY, folding one side and then repeating it exactly on the other, and on turning the square into a TRIANGLE or a smaller square as a base.
Folding can do what rulers cannot
For more than two thousand years mathematicians tried to split any angle into three equal parts using only a compass and a straight edge, and in 1837 it was finally proved impossible. With paper folding it can be done, because a single fold can do things a compass and ruler cannot. Mathematicians have since written down the basic moves a fold can make, and use them to prove which shapes are possible.
A common claim is that nobody can fold a piece of paper in half more than seven times. In 2002 a high-school student, Britney Gallivan, worked out the maths of why, then folded a very long strip of thin paper in half twelve times. Engineers use origami ideas too: fold patterns let solar panels and telescope shields be packed tightly into a rocket and opened out in space.
A thousand cranes
The CRANE is the best-known model, a symbol of long life and good fortune in Japan, and a tradition holds that folding a thousand of them brings a wish. The custom became known worldwide through Sadako Sasaki, a girl who was two when the atomic bomb fell on Hiroshima and developed leukaemia ten years later. She folded cranes in hospital before she died in 1955, and a statue of her holding a golden crane stands in the Hiroshima Peace Park, where children still leave strings of paper cranes.
Other favourites in the grid are the jumping FROG, the LOTUS, the STAR, the BOX, the FLOWER, the HEART and anything with WINGS. A good first model is the simple cup, which takes about six folds and really does hold water for a minute or two.