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Food and Grace
I stumbled on a post on X this morning, a commentary on the photo of RFK eating food from McDonalds that has been making the rounds. This photo divides Puritans from Southerners. Puritans think because RFK Jr is on the side of health food he can never commit such a “sin.” Southerners think a rare
Linear combination of sine and cosine as phase shift
Here's a simple calculation that I've done often enough that I'd like to save the result for my future reference and for the benefit of anyone searching on this. A linear combination of sines and cosines a sin(x) + b cos(x) can be written as a sine with a phase shift A sin(x + φ).
The Postage Stamp Problem
I recently stumbled upon the Postage Stamp Problem. Given two relatively prime positive numbers a and b, show that any sufficiently large number N, there exists positive integers x and y such that ax + by = N. I initially missed the constraint that x and y must be positive, in which result is well
Channel capacity of a telegraph
Claude Shannon's famous paper A Mathematical Theory of Communication [1] includes an example saying that the channel capacity of a telegraph is log2 W where W is the largest real root of the determinant equation Where in the world did that come from? I'll sketch where the equation above came from, but first let's find
Limitations on Venn diagrams
Why do Venn diagrams almost always show the intersections of three sets and not more? Can Venn diagrams be generalized to show all intersections of more sets? That depends on the rules you give yourself for generalization. If you require that your diagram consist of circles, then three is the limit. As John Venn put