Instead of using origami to explore new ideas in mathematics, some researchers have used mathematical frameworks to explore new ideas in origami. Or perhaps your questions will lead you in the opposite direction. Then, for a truly mind-bending journey, you might land on the concept of higher-dimensional symmetric shapes. These 3D shapes have a lot of symmetry, though not as much as the Platonic solids. Questions about larger models will lead you to the Archimedean solids and the Johnson solids. Questions about coloring will lead you to the mathematics of graphs and networks (and big questions that remained unsolved for many centuries). One seemingly innocent question can easily lead to a mathematical rabbit hole. Once you’ve mastered the basic structure of each 3D shape, you may find yourself (as others have done) pondering deeper mathematical questions.Ĭan you arrange the sonobe units so two units of the same color never touch, if you only have three colors?Īre larger symmetric shapes possible? (Answer: yes!)Īre there relationships between the different 3D shapes? (For example, the icosahedron is basically built of triangles, but can you spot the pentagons lurking within? Or the triangles in the dodecahedron?) Sonobe units, like these ones piled in a stack, can be put together to create 3D shapes. I’ve got written instructions for building the cube on my website, and some quick searching online will find you instructions for the larger models. (Interestingly, it’s not possible to build a tetrahedron and dodecahedron from sonobe units). You will need six sonobe units to make a cube like the yellow-blue-green one pictured above, 12 to make an octahedron (the red-pink-purple one), and 30 to make an icosahedron (the golden one). Sonobe units are fast and simple to fold, and can be fitted together to create beautiful, intriguing 3D shapes like these: I’ve got instructions for how to make a sonobe unit on my website and there are plenty of videos online, like this one: to make a sonobe unit. To build Platonic solids in origami, the best place to start is to master what’s known as the “ sonobe unit“.Ī sonobe unit (sometimes called the sonobe module) looks a bit like a parallelogram with two flaps folded behind. While there are infinitely many regular polygons, there are, surprisingly, only five Platonic solids: This model, folded by the author, uses a design from the book “Perfectly Mindful Origami - The Art and Craft of Geometric Origami,” by Mark Bolitho. The Platonic solids are 3D shapes made from regular 2D shapes (also known as regular polygons) where every side and angle is identical: equilateral triangles, squares, pentagons. They’re named after the ancient Greek philosopher Plato (although they almost certainly predate him and have been discovered in ancient civilisations around the world). In mathematics, the shapes with the most symmetry are called the Platonic solids. They require no mathematical background but will take you in some fascinating mathematical directions. My website Maths Craft Australia contains a range of modular origami patterns, as well as patterns for other crafts such as crochet, knitting and stitching. Once you’ve mastered the basic structure of a 3D shape, you may find yourself pondering deeper mathematical questions. So, for a little effort you are rewarded with a vast number of models to explore. Many modular origami patterns, although they may use different units, have a similar method of combining units into a bigger creation. The building blocks, called units, are typically straightforward to fold the mathematical skill comes in assembling the larger structure and discovering the patterns within them. That’s where you use several pieces of folded paper as “building blocks” to create a larger, often symmetrical structure. Any piece of origami will contain mathematical ideas and skills, and can take you on a fascinating, creative journey.Īs a geometer (mathematician who studies geometry), my favorite technique is modular origami. I’m a mathematician whose hobby is origami, and I love introducing people to mathematical ideas through crafts like paper folding. Many of us could happily fold a paper crane, yet few feel confident solving an equation like x³ – 3 x² – x + 3 = 0, to find a value for x.īoth activities, however, share similar skills: precision, the ability to follow an algorithm, an intuition for shape, and a search for pattern and symmetry.
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