By George Hart for the Museum of Mathematics
What could sound easier than to make a regular construction from four paper equilateral triangles? One possible construction is the regular tetrahedron, which is pretty easy. Here is a different construction from four equilateral triangles. Each triangle is linked with the other three, like two links of a chain.
Use this template, in which each triangle has a hole cut from it, with exactly half the edge length. You’ll need to cut through three of them to link them together. After you assemble them properly, you can tape the cut back together.
Cory Poole took this idea and miniaturized it, making a lovely pair of geometric earrings from paper painted with metallic paint.
Instructions for assembling the triangles are available here, along with other polygon assembly challenges.
More:
See all of George Hart’s Math Monday columns
10 thoughts on “Math Monday: Four Paper Triangles”
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In origami:
http://www.flickr.com/photos/mancinerie/4468779757
and in pencilrs+ubber bands
http://www.flickr.com/photos/mancinerie/6069571573
The origami and pencil ones in the comment are really cool. I’m also commenting because I’m Cory (not Corey :) ) Poole.
Sorry about that Corey… er… Cory. Fixed!
Hah! It’s ok. I’m used to it.
Print twice, than make the cut on each set on a different place, mount together and glue than!