John    Suppose you have a calculator or math library that only handles real arguments but you need to evaluate sin(3 4i). What do you do? If you’re using...

John    The hardest part of using regular expressions is not crafting regular expressions per se. In my opinion, the two hardest parts are minor syntax...

John    The previous post introduced the idea of a twelve-tone row, a permutation of the twelve pitch classes of a chromatic scale. The earlier post also...

John    The previous post looked at why Mathematica does not simplify the expression Sinh[ArcCosh[x]] the way you might think it should. This post will be a...

John    Let p be a prime number. Then the integers mod p form a finite field. The number of elements in a finite field must be a power of a prime, i.e. the...

John    Last week I gave an example of a randomly generated fractal and mentioned that it was a particularly special case of a more general algorithm for...

John    The previous post began by saying Bitcoin’s Wallet Import Format (WIF) is essentially Base58 encoding with a checksum. More specifically, WIF uses...

John    The previous post explained why the Gregorian calendar is the way it is, and that it consists of a whole number of weeks. It follows that the...

John    Marc Stevens gave an example of two alphanumeric strings that differ in only one byte that have the same MD5 hash value. It may seem like beating a...

John    The key to solving a lot of elementary what-number-comes-next puzzles is to take first or second differences. For example, if asked what the next...

John    Fermat’s little theorem says that if p is a prime number, then for any positive integer b p we have bpâ ’1 1 (mod p). This theorem gives a necessary...

John    I needed the inverse factorial function for my previous post. I was sure I’d written a post on computing the inverse factorial, and intended to reuse...

John    A Kepler triangle is a right triangle whose sides are in geometric progression. That is, if the sides have length a b c, then b a c b k. All Kepler...

John    The previous post describes the hoops I jumped through to enter Unicode characters on a Mac. Here’s a script to run from the command line that will...

John    I was flipping through Gravitation [1] this weekend and was curious about an illustration on page 309. This post reproduces that graph. The graph is...

John    Given the equations for two circles, how can you tell whether they intersect? And if they do intersect, how do you find the point(s) of intersection?...

John    Yesterday I wrote about how you could use the spaCy Python library to find proper nouns in a document. Now suppose you want to refine this and find...

John    Suppose you take the arithmetic mean and the geometric mean of the first n integers. The ratio of these two means converges to e 2 as n grows [1]. In...

John    Let Ï be the golden ratio. The fractional parts of nÏ bounce around in the unit interval in a sort of random way. Technically, the sequence is quasi...

John    I used Mathematica to create the graphics for my previous two posts because SciPy didn’t have the functions I needed. In particular, elliptic...

John    Thanks to the quadratic equation, it’s easy to tell whether a quadratic equation has a double root. The equation has a double root if and only if the...

John    This post is for someone unfamiliar with SciPy who wants to use Python to do basic statistical calculations. More specifically, this post will look...

John    There are 10 digits in ASCII, and I bet you can guess what they are. In ASCII, a digit is a decimal is a number. Things are much wilder in Unicode....

John    ICD codes are diagnostic codes created by the WHO. (Three TLAs in just the opening paragraph ) The latest version, ICD-11, went into effect in...

John    I had some errors in a recent blog post that might have been eliminated if I had programmatically generated the content of the post rather than...

John    I’ve had to work a little with VIN numbers lately, and so I looked back at a post I wrote on the subject three years ago. That post goes into the...

John    I got a data file from a client recently in pickle format. I happen to know that pickle is a binary format for serializing Python objects, but trying...

John    With org-mode you can keep data, code, and documentation in one file. Suppose you have an org-mode file containing the following table. # NAME...

John    The previous post discussed how to use org-mode as a notebook. You can have blocks of code and blocks of results, analogous to cells in a Jupyter...

John    You can think of org-mode as simply a kind of markdown, a plain text file that can be exported to fancier formats such as HTML or PDF. It’s a lot...