The other day I was browsing a book on Mayan Civilization and Archeology and was reading about their base-20 number system and how it was juxtaposed to their calendar system in terms of complexity. I started to play a bit with the number system (I love messing about mathematically in different bases — place-value systems are so brilliant!). Thinking of the prog-rock band Rush’s palindromic album title, 2112, I quickly converted in my head and came to a surprising conclusion:
The number twenty-one twelve is a palindrome in both Hindu-Arabic base-ten numerals: and in Mayan base-twenty numerals:
However, Mayan is normally written along the vertical axis rather than the horizontal:
Granted, it is a palindrome only graphically, as transliterating to Hindu-Arabic numerals would give us 5.5.12 (base 20, using decimals as place separators), not exactly palindromic. Even so, I thought this was a neat observation.
Showing posts with label mathematics. Show all posts
Showing posts with label mathematics. Show all posts
Tuesday, July 8, 2014
2112 in Mayan
Labels:
mathematics,
Mayan,
number systems,
palindrome
Sunday, May 12, 2013
Physical Color Space
While working on the GIS project I described in this post, I had a presentation conundrum: how do I communicate my mapping of RGB (Red, Green, Blue (additive)) color space to ideology symbology to an audience that may or may not have only a passing acquaintance with the physics of color and how it relates to our current computer technology. To solve this issue, I decided I could physically model RGB space as a cube.
The cube allows one to examine the outer surface of the RGB space; as well as illustrating the relationship between additive and subtractive spaces. In terms of my ideological representation issue, I was able to communicate that the 3-axes used to represent Red, Green, and Blue values could be relabeled to represent the percent of the vote supporting Conservative, Alternative, and Liberal ideologies.
Licensed under Creative Commons: BY-NC-SA
The cube allows one to examine the outer surface of the RGB space; as well as illustrating the relationship between additive and subtractive spaces. In terms of my ideological representation issue, I was able to communicate that the 3-axes used to represent Red, Green, and Blue values could be relabeled to represent the percent of the vote supporting Conservative, Alternative, and Liberal ideologies.
Now I’m sharing, so you can make your own. You’ll need:
- a color printer or access to one.
- some poster board or other heavy (but flexible) art board
- an Xacto knife or other cutting implement.
- a ruler
- a pencil
- glue-stick, or other paper adhesive.
After printing, cut out and trace on to the art board one of the following PDFs (remember to add tabs if using the original PDF):
- Here’s the original PDF;
- and if you want to hide the edges, here’s one with tabs.
Next, you’ll cut out and fold the art board into a cube being sure to tuck the tabs in, so you have a more-or-less smooth external surface.
Then you’ll want to do the same with the color print-out, only this time gluing it to the art board cube you’ve assembled. (Again, remember to tuck any tabs underneath.)
Optionally, you may attempt to cover your creation with a protective covering (this usually doesn’t go as well as one would like — I wrapped mine in packing tape, but it got blisters and a tiny patch of color torn, etc.)
Cube size is approx. 2.75"^3Licensed under Creative Commons: BY-NC-SA
Labels:
cartography,
color,
mathematics,
space
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