Author: John

Spherical trig, Research Triangle, and Mathematica

This post will look at the triangle behind North Carolina’s Research Triangle using Mathematica’s geographic functions. Spherical triangles A spherical triangle is a triangle drawn on the surface of a sphere. It has three vertices, given by points on the sphere, and three sides. The sides of the triangle are portions of great circles running […]

Visualizing data breaches

The image below is a static screen shot of an interactive visualization of the world’s biggest data breaches. The site lets you filter the data by industry and type of breach. See the site for credits and the raw data.

Topping out

There’s an ancient tradition of construction workers putting a Christmas tree on top of a building when it reaches its full height. I happened to drive by a recently topped out building this morning.

Complex exponentials

Here’s something that comes up occasionally, a case where I have to tell someone “It doesn’t work that way.” I’ll write it up here so next time I can just send them a link instead of retyping my explanation. Rules for exponents The rules for manipulating expressions with real numbers carry over to complex numbers […]

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 […]

My Twitter graveyard

I ran into The Google Cemetery the other day, a site that lists Google products that have come and gone. Google receives a lot of criticism when they discontinue a product, which is odd for a couple reasons. First, the products are free, so no one is entitled to them. Second, it’s great for a […]

Poetic description of privacy-preserving analysis

Erlingsson et al give a poetic description of privacy-preserving analysis in their RAPPOR paper [1]. They say that the goal is to … allow the forest of client data to be studied, without permitting the possibility of looking at individual trees. Related posts What is differential privacy? Data privacy consulting [1] Úlfar Erlingsson, Vasyl Pihur, and […]

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 […]

All possible scales

Pete White contacted me in response to a blog post I wrote enumerating musical scales. He has written a book on the subject, with audio, that he is giving away. He asked if I would host the content, and I am hosting it here. Here are a couple screen shots from the book to give […]

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 […]

Sequence alignment

In my previous post I illustrated the Levenshtein edit distance by comparing the opening paragraphs of Finnegans Wake by James Joyce and a parody by Adam Roberts. In this post I’ll show how to align two sequences using the sequence alignment algorithms of Needleman-Wunsch and Hirschberg. These algorithms can be used to compare any sequences, though they […]