Entropic Thoughts
2 days ago
- Pythagorean addition (√(a² + b²)) is common in geometry, statistics, and physics, but mentally computing it is difficult.
- The alpha-max plus beta-min algorithm estimates √(a² + b²) as max(a, 0.9a + 0.5b) with a maximum error of 3%, enabling easy mental calculation.
- The method can be inverted to estimate the larger component from the total and the smaller component using formulas like â = 2(c - 0.9b) or â = 1.11(c - 0.5b).
- An example combining standard deviations of height between sexes and within groups gives a total variation of about 9.3 cm.