Appreciation Geometry
An Accidental Valentine
The fact that we were discussing concave, orthodiagonal quadrilaterals on February 14th provided some incidental amusement.
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Appreciation Geometry
Tiling at IKEA
I got a bit bored on a recent trip to IKEA, so I started looking for mathematical things to play around with. I quickly found this octagon.
There were plenty available, so I started tiling the plane.
Unfortunately, I didn’t have time to finish.
Appreciation Geometry
Torus Games
Ever wonder what it would be like to play chess on a donut? Well, wonder no further: here’s a free set of simple games all redesigned to be played on a torus.
http://www.geometrygames.org/TorusGames/
A torus is a geometric surface that is basically equivalent to a donut (the surface of the donut; not the interior). One way to [theoretically] construct a torus is to take a flat piece of paper, roll it into a cylinder by gluing the two opposite edges together, and then curling the cylinder into circle and gluing the two circular ends of the cylinder together.
So how do you play pool on a torus? As the image to the right suggests, if you shoot the ball toward the top edge of the table, it will wrap around and come out the bottom. The sides similarly wrap around, too.
This strange geometry definitely creates new strategic options in Chess and Tic-Tac-Toe, and this free set of games also include Word Search and Crossword.
A simple, thought-provoking idea. And free and fun to boot!
Appreciation Art Geometry
3D Street Art
The painter Edgar Mueller uses dilation and perspective tricks to create absolutely mind-blowing three-dimensional pavement art.
The website is a little clumsy, but there are some really cool projects here, including The Crevasse, The Waterfall, and Lava Burst. There are also several videos showing how the artist puts these perplexing pavement paintings together.
For an interesting application of this idea, check this out: a 3D pavement painting of a child playing in the middle of the street! The idea was to get the attention of speeding drivers. I bet it did just that!