In this post, we’re going to try to approximate the error function, which is a very important function in statistics and also a fascinating function overall. I wanted to make this post for a long time now because it combines ideas from mathematics and computer science, and it even introduces a new idea as well! If you are ready, let’s dive in. If you don’t remember, the error function is defined as below.

Some time ago, I wanted to find a formula for a function that passes through a given set of points. And since I love reinventing the wheel, I decided to not google the problem and instead find a formula of my own. Let \(f(x)\) to be the function we are looking for and \(\{(x_{i}, y_{i}) \mid i=1,2,\dots,n \}\) to be the given set of points. My strategy was to express the function as a sum of \(n\) distinct functions \(f_{i}(x)\), each satisfying the properties below.

In 2021, I was playing a lot of bedwars games with a friend of mine. We played rather well together and when we got bored with playing competitively, we started trolling other bedwars players. We’ve done a lot of trolls, but one of them was building obscure bed defenses. For example the defense below is called “The Éclair Defense” and it contains obsidian in its first layer, glass (or clay for some servers) in its second layer and wool for its last layer.