I wrote six blog posts this weekend, and they’re all related. Here’s how.
Friday evening I wrote a blog post about a strange random number generator based on factorials. The next day my electricity went out, and that led me to think how I would have written the factorial RNG post without electricity. That led to two threads: interpolation in tables and calculations with floors.
The interpolation thread has two posts. The first looks at error estimates for polynomial interpolation, and shows that numerical error can easily dominate approximation error in interpolation. The second looks shows that interpolation for tables of sines and cosines can be better than interpolation in general.
The floor calculation thread first lead to this post which states a useful theorem from Concrete Mathematics and uses a slight generalization of the theorem to justify a numerical calculation. Then a comment on an earlier post led to a new post giving simple and tight bounds on the number of trailing zeros in a factorial.
You can read each of these posts by itself, but I thought some people would appreciate seeing how they fit together.