Thursday, August 04, 2005

Numeric Patterns

We see certain patterns in numbers due to our base 10 number system. If we looked at all numbers, say, in base 6, binary, or hex, the patterns would be significantly different.

For example, the numbers 1000, 2000, and 3000, all fit a simple pattern, right? A ten year old could figure out the difference between each number in the pattern is 1000. Let's convert these numbers into hex:
3E8
7D0
BB8
They are in no way the same pattern. The difference is still the same (3E8 in hex), but it's just not special any more.
Imagine how different things would be with a different number system. I mean, you might only have "10 minutes" on your break still, but in decimal, that's 16. We pick numbers like 10, 15, 5 all because they're evenly rounded in our number system, but in hex you'd be much more likely to pick 10, 18, 8, etc., which are 16, 24, and 8 in decimal.

24 probally does sound more familiar to you; it's the number of hours in a day. The number 24 was chosen because our calendar was invented by people with a base 6 number system. 24 in base 6 is 40. Same with 360 degrees being the basis of geometry (thank God radians came around), the people who created it based it upon their number system, and therefore, it's somewhat awkward in our system.

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