Three proofs, just to be sure. In this article we will see various ways to prove Euler’s formula and Euler’s identity. Euler’s formula Euler’s formula is:

The Cantor set is one of the simplest fractals, and also one of the earliest to have been studied in detail. As a one-dimensional structure, it was easy to visualise before modern computers were available. History of the Cantor set Georg Cantor is best known for his work on early set theory. One of his…

We are all familiar with base 10 numbers (denary). And if you have ever done any computer programming you will also be familiar with base 2 numbers (binary). This article is about trinary numbers (sometimes called ternary numbers). Trinary numbers use base 3. Why study these numbers? Well, one important…

The first derivative of the sine function is the cosine function:

We tend to think of binary numbers as being a modern concept developed as part of computer science. But in fact, some elements of the binary system were known in ancient times, because they were very useful in many fields back then. This article explains how binary numbers work, but…

A graph is often represented by a graph diagram like the one on the left, below:

Some infinite sets are more infinite than others. A set is a collection of objects. In this article, we will look at how we go about counting the elements in a set. In particular, we will investigate how we might count the elements in an infinite set, and if that…

The result is quite surprising! The imaginary unit is defined to be the positive square root of -1. But what is to the power i? Is it even possible to calculate, and what does it mean? As we will see, it is possible to calculate i to the power i…

The product rule allows us to find the derivative of the product of 2 or more functions. It provides a simple way to differentiate functions such as: