Did you know that Origami, an ancient paper folding art, is of interest to scientists, mathematicians, and engineers because of its ability to transform? Using Origami, you can collapse structures, fold them, flex them, and unfurl them at will. How many other things can do all of that?
Paper – At least 3 square pieces (1 for ghost and 2 for cat). A good size to start with is 8½ x 8½ inches, but you can try others. Plain office paper weight or just slightly thicker is good.
Optional – String, tape, and pencil, pen, or markers to decorate your creatures.
Note: Traditional origami paper has different colors or patterns on each side. We have used two-tone paper here for clarity, but it is not required. Follow the first rule of origami: You can only use one sheet of paper, and you can’t make any cuts in it.
Copyright: Fumiaki Shingu
To make a traditional cat (from diagrams by Francesco Mancini and Francesco Decio), you will need two squares of paper for this creation.
Origami is an excellent example of the intersection of math and art. The word “origami” comes from the Japanese words for “fold” and “paper.” The origins of origami are muddled, but paper folding traditions existed throughout Asia and Europe. Origami is closely related to the mathematics of geometry. In Ancient Greece, Euclid, a mathematician, defined a type of geometry based on using tools like a compass and straightedge. His math relied on points and lines, and it was useful, but there were two problems Euclidean geometry could never solve: trisecting an angle and doubling a cube. It would take a long time before we found solutions; origami wasn’t used for mathematics originally.
Now we know that Euclidean geometry can only be used to solve second degree equations while origami can solve third degree equations. So, origami can be used to draw any line that Euclid’s math could and then some! In 1989 and 1991, two different mathematicians developed axioms of origami (Huzita-Justin axioms)—statements that are proven to be true and serve as a basis for further reasoning. These mathematics-backed statements help others create new structures.
Computers made things even more interesting! An American physicist, Robert Lang, led the charge into computational origami, and he has written computer programs that design origami structures. He wonders if computers may be able to make more intricate designs than humans. Dr. Lang used origami techniques to make airbags in cars safer! Origami techniques have also been applied to solar arrays, medical devices, and architecture.
Origami offers great tactile and spatial reasoning experience when studying geometry. It also requires practice, patience, and precision and leaves you with beautiful art as well as enhanced mathematics knowledge!