Category: Math

Sine sum

Sam Walters posted something interesting on Twitter yesterday I hadn’t seem before: The sines of the positive integers have just the right balance of pluses and minuses to keep their sum in a fixed interval. (Not hard to show.) #math pic.twitter.com/RxeoWg6bhn — Sam Walters ☕️ (@SamuelGWalters) November 29, 2018 If for some reason your browser […]

Searching for Mersenne primes

The nth Mersenne number is Mn = 2n – 1. A Mersenne prime is a Mersenne number which is also prime. So far 50 51 have been found [1]. A necessary condition for Mn to be prime is that n is prime, so searches for Mersenne numbers only test prime values of n. It’s not sufficient for n to be prime […]

Searching for Fermat primes

Fermat numbers have the form Fermat numbers are prime if n = 0, 1, 2, 3, or 4. Nobody has confirmed that any other Fermat numbers are prime. Maybe there are only five Fermat primes and we’ve found all of them. But there might be infinitely many Fermat primes. Nobody knows. There’s a specialized test for […]

Geometry of an oblate spheroid

We all live on an oblate spheroid [1], so it could be handy to know a little about oblate spheroids. Eccentricity Conventional notation uses a for the equatorial radius and c for the polar radius. Oblate means a > c. The eccentricity e is defined by For a perfect sphere, a = c and so e = 0. The eccentricity for earth is […]

Ellipsoid distance on Earth

To first approximation, Earth is a sphere. But it bulges at the equator, and to second approximation, Earth is an oblate spheroid. Earth is not exactly an oblate spheroid either, but the error in the oblate spheroid model is about 100x smaller than the error in the spherical model. Finding the distance between two points […]