Houston, we have nonagons! The house that we just stayed at on the beach, the one with the neat-looking but nonfunctional Tide Clock, redeemed itself mathematically by having glasses in the shape of nonagons:
Does that look like I faked it? Here’s the unedited picture, in case you don’t believe me:
And just so the other polygonal glasses don’t get jealous, there was also a hexagon glass:
These join the decagon mug in the polygonal kitchenware Hall of Fame.
Nanotubes are back in the news! Nanotubes are sheets of carbon atoms, one atom thick, that roll up to form strong cables for tennis rackets and baseball bats. Very strong cables, in turns out, as in a possible material for a space elevator.
But even if the space elevator doesn’t work out, it turns out that carbon nanotubes can be used to make near-ideal black objects: things which absorb light completely, not refracting any of it. ‘Darkest Ever’ Material Created on BBC News in January explains that this is useful for creating solar cells and solar panels.
So what does does this have to do with mathematics? Quite a bit, if you look on wikipedia or if you actually build anything physical with it. But even at a simpler level, one neat property is that the carbon atoms bind in hexagons. You can see that in the picture below of a hexa-tert-butyl-hexa-peri-hexabenzocoronene. (How’s THAT for a word?)
The hexagons in the picture above are regular hexagons, meaning that all the sides and all the angles are equal. You can completely tile a plane with regular hexagons, without leaving any gaps. And this means that the hexagons in the carbon nanotubes must not be exactly perfectly regular, or else there would be no way for them to roll up. Either the angles or the sides must be a little off.
This irregularity doesn’t actually harm the carbon nanotubes. Unfortunately, they have bigger problems right now: BBC news reported Tuesday that when some fibers got into the lungs of mice, they caused inflammation and legions, like asbestos. Poor nanotubes. That doesn’t sound the death knell, however; it’s only one study, and so more research, more money, etc. etc. have to be dedicated to the topic. But it might be a while before we see that solar-powered space elevator.
Pictures used under GNU Free Documentation License.
The Giant’s Causeway (Clochán na bhFómharach: the little stone pile of the Fomorians) off of northeast coast of Northern Ireland was formed many years ago by the giant Finn MacCool, as explained here. An alternate theory has it being formed sixty million years ago by lava cooling quickly (possibly by coming into contact with water) after a volcanic explosion. We may never know for sure which of those stories is true, but what is true is that a lot of the basalt rocks formed into hexagonal columns.
Photo by code poet; licensed under Creative Commons Attribution ShareAlike 2.0
I’d heard of these rocks before, but encountered them again in a photo by Lyn Miller under Found Math on MAA Online. Her photo was taken at Devils Postpile National Monument in California near Yosemite, which also has an impressive array of columns that average two feet in diameter.
Photo by Daniel Mayer; licensed under Creative Commons Attribution ShareAlike 1.0
Finally, if you google “hexagon lava” you find posts like this. It gives Lava Lamp a whole new meaning.
I was about to post about the interesting shapes in the cookie cake tops at our grocery store (which I’ll do shortly), and I found myself getting distracted thinking about all of the interesting shapes in the snack aisle itself. (more…)
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