Floating through the nodegel today, I started reading through Johnath's writeup on combinatorial explosion when I came across this phrase in his calculations. Being the math nerd that I am, I just found this too cool to pass up, so I worked it out for myself:
10-9 centuries × 100 years/century × 365.25 days/year × 24 hours/day × 60 minutes/hour × 60 seconds/minute
Percent error from π seconds: |3.15576 - π|/π = 0.45%
Naturally, I find this to be pretty damn cool. If anything, it makes a great mnemonic, but I have to wonder if there are any other strange wonderful coincidences like this in our unit system. I bet e feels jealous.
An example of this in use (at the request of m_turner, who also informs me that this conversion factor can be found in Programming Pearls) would go something like this: Suppose you have a program that needs to execute 108 instructions, and each instruction takes 1/3 of a second. How long would the program take to execute? Of course, you could run through all the conversion factors from seconds to years, but who wants to do that?
108 instructions × 1/3 seconds/instruction × 1/π nanocenturies/second × 10-9 centuries/nanocentury × 100 years/century