Pythagorean Addition
2 days ago
- #approximation
- #mathematics
- #mental calculation
- The alpha-max plus beta-min algorithm provides a simple mental approximation for calculating the Pythagorean sum \(c = \sqrt{a^2 + b^2}\).
- Assuming \(a\) is the larger number, estimate \(\hat{c} = 0.9a + 0.5b\), and if it's less than \(a\), use \(\hat{c} = a\). This method has an average error of 1.5% and worst-case error of 3%.
- The approximation is useful for adding sources of variance, such as in statistics, geometry, and physics, making mental calculations more intuitive.
- The algorithm can be inverted: given \(c\) and \(b\), approximate \(\hat{a}\) as \(2(c - 0.9b)\) or \(1.11(c - 0.5b)\), depending on term sizes.
- An example application: estimating total height variation by adding gender and within-group standard deviations, yielding a quick mental result.