Decorate for Halloween—or anytime—with these crafty creations made by careful paper folding.
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?
You will need:
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.
Make an Easy Ghost
Copyright: Fumiaki Shingu
- Start with a square piece of paper. The size does not matter.
- Fold the square in half diagonally by bringing two opposing corners together. Push down along the fold well to crease. When you open the paper back into a square, you should see a line left behind by the fold. That is a good crease!
- Open your square and turn the paper so the crease is in the middle and perpendicular to your chest. The paper should now look like a diamond.
- Fold the left and right corners in so the bottom half of the diamond gets skinnier and the points of the corners meet the center line. The paper now looks like an ice cream cone.
- On each side, one at a time, fold the corners that you just folded in back out at an angle to create the ghost’s hands.
- Take one of the corners where the ice cream meets the cone and fold it in to meet the center crease. Do the same on the other side.
- Fold the point at the top down until the fold meets the top points left by the previous folds. This should make a straight edge for the top of the head. If desired, fold the bottom corner on an angle about an inch up to make a unique tail.
- Turn your creation over and give your creation a ghostly face! You might also want to punch a hole in the top of the head so your ghost can “hang around,” or simply tape some string onto the back of the ghost. Would you like it to float on its side? Think about how you would like it to hang and where you would need to put the string to balance it that way when it is hanging!
Make a Cat
To make a traditional cat (from diagrams by Francesco Mancini and Francesco Decio), you will need two squares of paper for this creation.
- To begin the head, fold one square of paper in half diagonally and crease well. Repeat for the other diagonal. When you open your square, you should see two crease lines that divide the square into four triangles.
- Fold the paper along one of the diagonals and point the bottom of the triangle, where the two corners of the square meet, toward you. Fold the left and right corners over and down so the two points of those corners meet the point at the bottom and their edges align with the center crease. The paper should now look like a small diamond.
- Fold the two flaps up and out until the fold reaches the corners of the diamond. Crease well. These are the cat’s ears.
- Fold the top of the diamond down between the ears until the fold meets the ears. This should make a straight edge for the top of the head.
- Flip the head over. The bottom of the head, where the chin would be, should be two corners of the original square. Fold one up until the point hits the center of the face. The inner color of your paper, if you have one, should be showing. Fold the other point the same way but to the back of the head. This should leave a pocket on the bottom of the head.
- On the front of the head, fold the corner in the middle of the face back down to meet the chin to make a nose. Crease well. Draw a face on your cat head.
- For the body, use a new paper square. Fold the page in half diagonally once and crease well.
- Turn the page so one of the shorter edges of the triangle is parallel to the table edge. Fold the bottom corner of the triangle in to make a tail.
- Stand the body up on the table so the tail is along the table.
- Open the pocket on the head and slide the head over the top corner of the body. Now you have a free-standing origami cat!
What’s going on?
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!