Math on redlegion.orghttps://redlegion.org/tags/math/Recent content in Math on redlegion.orgHugo -- gohugo.ioenFri, 26 Aug 2022 00:10:15 +0000Totientshttps://redlegion.org/2022-08-04/totients/Thu, 04 Aug 2022 08:19:20 -0400https://redlegion.org/2022-08-04/totients/In the past, I’ve implemented Euler’s totient function for shits and giggles. It’s not a hard exercise by any means, but it can be if you haven’t had education in math at a level to understand the formula.
$$\varphi(n) =n \prod_{p\mid n} \left(1-\frac{1}{p}\right)$$
Admittedly, I had to google what the hell is going on. Technically, that’s just the framework, there are more details that follow in the form of rules. However, it was definitely a fun exercise to implement it.Unit Vectors and Angleshttps://redlegion.org/2022-08-03/unit-vectors-and-angles/Wed, 03 Aug 2022 12:45:44 -0400https://redlegion.org/2022-08-03/unit-vectors-and-angles/In my job, I work with a ton of unit vectors. While tracking things in three dimensions can be tricky, it helps to start breaking down as many aspects of the dimensions to their base components. I’m sure we’re all familiar with common spatial axis labeling. You get X, Y, and Z. Their application isn’t uniform. Some machine uses X for the vertical axis, some might use Z. What you might not yet be familiar with would be the orientations of objects in space.Statisticshttps://redlegion.org/2013-10-27/statistics/Sun, 27 Oct 2013 11:38:55 +0000https://redlegion.org/2013-10-27/statistics/Statistical Analysis of Variance. Using standard deviations six times higher and six times lower than your target, determine whether your process is “in control” or “out of control”. Good stuff.
It’s also part of the framework for determining the reproducibility and repeatability of gaging. I’ve discovered that Minitab is one of the best software suites for achieving what you need in calculating ANOVA for your GR&R. It’s a great deal faster than laying out your own Excel spreadsheet, and it allows you to completely automate the process.