Is your family snowbound in Saskatchewan? Heatbound in Gila Bend? Stave off cabin fever in entertaining and educational fashion with some geometry activities that are free of charge and available at the mere tapping of your fingers.
HyperGami offers a series of colorful projects to print on cardstock, cut, fold and glue into the shapes of (in order of increasing difficulty) fish, a turtle, a cat, and a train. The instructions gently insert instruction on the nature of the shapes being used and their geometric significance. The results are purty. If you want more after you’re done with these entry-level examples, then check out the University of Colorado Computer Science Department’s free JavaGami software, which allows you to design and print your own paper model, challenging you to think about how various polyhedra can be used to simulate familiar objects.
Torus Games begin with familiar forms like Tic Tac Toe and billiards, but remove borders from them. This act changes gameplay fundamentally, and has the subtle and sneakily wholesome goal of getting users to appreciate the nature of surfaces that are “finite yet unbounded.”
Kali is a program that lets users who’ve never heard the word “tessellation” draw Escher-like designs in seconds. Kali’s intuitive interface begins with the choice of color and line thickness. Then users select one of a couple of dozen forms of symmetry, and they’re ready to go. A left-click starts a new section of a curve and a right-click finishes off a design. It’s a simple process that can produce results of enough beauty and variety to distract for hours. Hint: take a screen capture and import it into a highfalutin’ graphics program in order to add fill colors and otherwise add polish.
Kaleidotile has educational potential at the high-school level, with attached exercises and question sheets that guide the user along various lines of mathematical thought. But even an incurious tinkerer can have fun easily changing the value of a small set of variables — form of symmetry, curved or angular surface, relative size of faces and picture fill for faces — to create a surprisingly large range of polyhedra (from the tetrahedron, cube and icosahedron on up) or even a sphere. Click an option to have a helpful voice identify the names of the odd shapes you’ve just made. Even ignoring all those names, the results can be simply beautiful as they rotate in a simulated 3D space on your screen.
The above activities alone could stave off boredom and maintain neural integrity during a week of isolation. They’re available. They’re fun. They’re educational. They’re afeducational! Woo hooooooooo.