Do the Doodle Dome
One never knows what treasures can be found at garage sales, second-hand stores, or even on e-bay. A prime example for mathematics teachers is the Doodle Dome, which appears on a regular basis (e.g. two units are currently listed on e-bay).
First, the Doodle Dome was a Tyco toy sold in the early 1990's. Basically, it was an Etch-A-Sketch on a sphere rather than on a flat rectangle. Its two knobs move a little stylus around a spherical drawing surface, scraping off "silver dust" to reveal traces of lines--horizontal (latitudes), vertical (longitudes), and diagonals. With the flip of an additional lever, the user can lift the stylus point off of the surface and move it, so gaps can be created in a picture. It also includes a built-in 360 dsgree protractor for precise positioning of lines. To erase the full picture, the unit needs to be shaken (not stirred).
Over the past decade, I have purchased several Doodle Dome units in the regular and mini-sizes, usually for a sum less than $5. In addition to being a fun toy when I need a diversion, the Doodle Dome helps demonstrate the important properties of spherical geometry to my geometry students, such as why latitude lines stay parallel, but longitude lines converge, yet the angles between these lines remain 90 degrees.
But, as you might expect, some people push it beyond its apparent limit. For example, Sam Wintermute (MI) has "hacked" up his own Doodle Dome to produce computer-based arbitrary imaging. His Digitized Doodle Dome works with a PICAxe microcontroller, two 5.25-inch floppy drive stepper motors, a servo and other miscellaneous parts. Once set into motion, the unit takes about a day to produce a picture.
Some examples of his work are shown below, representing a model of the earth, a spherical checker-board, and a spiralized version of a long string of pi's digits:
For instructions on how this computer-drawing machine was built, consider Sam Wintermute's notes.