The other day, I found myself wondering how big 52! (52 factorial) is, and that led me to ponder how these could be estimated without a calculator or a computer. It turns out there’s some fairly interesting math behind being able to estimate the size (number of digits) of a factorial reasonably accu...

This is part 8 in a series of posts on writing concurrent network servers. In this part, we'll switch to Go and see how it tackles the challenges described earlier in the series. All posts in the series: Part 1 - Introduction Part 2 - Threads Part 3 - Event-driven Part 4 - libuv Part 5 - Redis case ...

This is part 7 in a series of posts on writing concurrent network servers. In this part, we discuss how the challenges described in earlier parts are tackled in the Rust programming language. All posts in the series: Part 1 - Introduction Part 2 - Threads Part 3 - Event-driven Part 4 - libuv Part 5 ...

In Physics simulations or game engines it’s sometimes useful to determine the speed with which two objects are approaching each other. This post will discuss the concept of closing speed, which is the normal component of the relative velocity of two objects. Relative velocity and its components Supp...

The Fourier series is a great tool for analyzing periodic functions. But what about functions that don’t repeat? We’ve seen that we can compute Fourier series for a non-periodic function defined on a finite interval, as long as we don’t care about its behavior beyond that interval. Let’s extend this...

The goal of this post is to answer a simple question: why are the following two definitions of the vector dot product in Euclidean space [1] equivalent for vectors \vec{a} and \vec{b}: Component definition: \vec{a}\cdot\vec{b}=\sum_{i=1}^{n}a_i b_i Geometric definition: \vec{a}\cdot\vec{b}=|\vec{a}|...