{"id":60965,"date":"2022-01-04T17:42:16","date_gmt":"2022-01-04T22:42:16","guid":{"rendered":"https:\/\/world.edu\/?p=60965"},"modified":"2022-01-04T17:42:16","modified_gmt":"2022-01-04T22:42:16","slug":"learn-how-to-make-a-sonobe-unit-in-origami-and-unlock-a-world-of-mathematical-wonder","status":"publish","type":"post","link":"https:\/\/world.edu\/learn-how-to-make-a-sonobe-unit-in-origami-and-unlock-a-world-of-mathematical-wonder\/","title":{"rendered":"Learn how to make a sonobe unit in origami \u2013 and unlock a world of mathematical wonder"},"content":{"rendered":"

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\nMany of us could happily fold a\u00a0paper crane<\/a>, yet few feel confident solving an equation like\u00a0x<\/em>\u00b3\u00a0\u2013\u00a03\u2009x<\/em>\u00b2\u00a0\u2013\u00a0x<\/em>\u00a0+\u00a03\u00a0=\u00a00, to find a value for\u00a0x<\/em>.<\/p>\n

Both activities, however, share similar skills: precision, the ability to follow an algorithm, an intuition for shape, and a search for pattern and symmetry.<\/p>\n

I\u2019m a mathematician whose hobby is origami, and I love introducing people to mathematical ideas through crafts like paper folding. Any piece of origami will contain mathematical ideas and skills, and can take you on a fascinating, creative journey.
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Once you\u2019ve mastered the basic structure of a 3D shape, you may find yourself pondering deeper mathematical questions. Julia Collins<\/p><\/div><\/p>\n

The \u2018building blocks\u2019 of origami models<\/strong><\/h4>\n

As a geometer (mathematician who studies geometry), my favourite technique is modular origami. That\u2019s where you use several pieces of folded paper as \u201cbuilding blocks\u201d to create a larger, often symmetrical structure.<\/p>\n

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.<\/p>\n

Many modular origami patterns, although they may use different units, have a similar method of combining units into a bigger creation.<\/p>\n

So, for a little effort you are rewarded with a vast number of models to explore.<\/p>\n

My website\u00a0Maths Craft Australia<\/a>\u00a0contains a range of modular origami patterns, as well as patterns for other crafts such as crochet, knitting and stitching.<\/p>\n

They require no mathematical background but will take you in some fascinating mathematical directions.
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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.
<\/p><\/div><\/p>\n

Building 3D shapes from smaller 2D units<\/h4>\n

In mathematics, the shapes with the most symmetry are called the\u00a0Platonic solids<\/a>. They\u2019re named after the ancient Greek philosopher Plato (although they almost certainly predate him and have been discovered in ancient civilisations around the world).<\/p>\n

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.<\/p>\n

While there are infinitely many regular polygons, there are, surprisingly, only five Platonic solids:<\/p>\n

    \n
  • the tetrahedron (four triangles)<\/li>\n
  • the cube (six squares)<\/li>\n
  • the octahedron (eight triangles)<\/li>\n
  • the dodecahedron (12 pentagons) and<\/li>\n
  • the icosahedron (20 triangles).<\/li>\n<\/ul>\n

    To build Platonic solids in origami, the best place to start is to master what\u2019s known as the \u201csonobe unit<\/a>\u201d
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    Sonobe units, like these ones piled in a stack, can be put together to create 3D shapes. Julia Collins, Author provide<\/p><\/div>.<\/p>\n

    Enter the sonobe unit<\/strong><\/h4>\n

    A sonobe unit (sometimes called the sonobe module) looks a bit like a parallelogram with two flaps folded behind.<\/p>\n

    I\u2019ve got instructions for how to make a sonobe unit\u00a0on my website<\/a>\u00a0and there are plenty of videos online, like this one:
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