Strange products upon running code...

[Mike Betts]

Back in the late 1970's and early 1980's (when I was in college) you learned a lot of tricks to make integer arithmetic work efficiently*.

Remember the Pi approximation by remembering the sequence 113355. Split into two different 3-digit integers and ask yourself if Pi is greater than or less than one? Voila! Pi = 355/113

Nowadays, there are tools to assist with computing ratios. I use Mathcad which will compute ratios and allow you to adjust for accuracy. As examples which are much harder to remember than Pi:

Sqrt(2) = 239/169 (or 577/408)
e = 193/71 (or 1264/465)

When applying any ratio in embedded systems, remember to multiply first and then divide and to watch for numeric overflows...

By the way, this numerical approximation was "discovered" over 2500 years ago (Google: Zu Chongzi or 113355)... All we had to do was to learn to apply it.

Mike

* The first computer I built from scratch had a Z80 (8-bit) processor running at 3.579545 MHz (NTSC color burst frequency). It took minutes to do any non-trivial math operations...