Here’s a fun use for a dodecahedron: folding it up to make a yearly calendar!
https://texample.net/tikz/examples/foldable-dodecahedron-with-calendar/
Just download the PDF, print, cut, fold, and glue! Access to a large-scale plotter might be nice, as the 8.5 x 11 version folds into something that’s pretty small.
It’s too bad there aren’t eight days in a week, otherwise we could put the octahedron to use, too!
I recently met some friends for dinner in an open-air food court underneath the New York City Highline. Much to my surprise, some arithmetic greeted us at the door.
Since beverages could not be purchased in cash, you first had to purchase beverage-vouchers which could then be exchanged for beverages. The beverage-vouchers only came in two denominations: $1 and $7.
I guess the food-court operators figured that most of their customers wouldn’t be comfortable solving stamp problems, so they were kind enough to provide some example solutions to common beverage equations.
This is a great set of photos depicting art made from the paths of Roomba robotic vacuum cleaners:
The paths traced out by these self-starting sweepers could provide a novel approach to random walking. And I wonder how much of the movement algorithm can be reverse-engineered simply by looking at a collection of paths?
It might be fun to perform experiments with roombas. For example, we could try to determine how long it takes one to completely traverse a floor, or how many times on average they pass through a given point. Or if working in tandem, what is the probability that two roombas collide?
Of course, we’d have to address the ethical issues of experimenting on roombas without their consent.
This is a truly mind-blowing idea: using the principle of natural selection to “evolve” a more efficient wind turbine blade.
http://www.youtube.com/watch?v=YZUNRmwoijw
Looking to see if he could somehow improve upon the standard blade design, a designer created a virtual world populated by blades of different shapes. He then “played god” by defining rules for reproduction between two blades.
Rules like “the most efficient blade gets first pick of mate”, and “the least efficient blades die” created a virtual world governed by the principle of natural selection, and after many generations, only the fittest, or most efficient blades. survived!
An unconventional blade emerged from the virtual world, but it passed the designers tests with flying colors, beating out the standard blade-design in efficiency. The blade looks strange, but it’s probably not the first odd-looking result of natural selection. After all, the camel is a weird-looking animal, but it gets the job done!
