In this post I will write a Python function to calculate sines using Taylor polynomials. It is impossible to calculate these directly but they can be approximated to any accuracy using this method, and I will show how a Taylor series converges to ever-increasing accuracy.Continue reading
One of the most useful bits of number-crunching you can do is to calculate the probability distribution of a set of data in the earnest hope that it will be a reasonable fit for one of the recognised distributions such as the normal distribution. In this project I will write a Python class to calculate the normal distribution for a given data set.Continue reading
I am currently working on an article about calculating sines and cosines using Taylor Polynomials. These make heavy use of factorials so I started thinking about ways to streamline the process.
This post consists of a simple project using memoization with a lookup table to pre-calculate factorials and store them for future use.Continue reading
This is a simple Python project demonstrating a useful application of logarithms. The logarithm of a number to a specified base is the power to which the base must be raised to get the number. Since their invention by John Napier in the 17th century until a few decades ago slide rules and books of log tables were used to simplify multiplication by turning it into a process of addition. Modern science, technology and engineering all depended on that simple idea.Continue reading
In this post I will develop a simple Python class to create and save an SVG (Scalable Vector Graphics) file, complete with a few examples of its use.Continue reading
This post will demonstrate programs which each perform a single very specific task but which can be chained together in such a way that the output of one forms the input of another. Connecting programs like this, or piping to use the correct terminology, enables more complex workflows or processes to be run.Continue reading
The graphic below shows a square with sides of length 2 containing a circle with a radius of 1. The area of the square is 4 and the area of the circle is 3.141592654 (sound familiar?!). The ratio of the area of the circle to the area of the square is 0.785398163 which is π / 4.
A while ago I wrote an article on estimating pi using various formulae, and in this post I will use the circle-within-a-square ratio illustrated above to run a stochastic simulation in Python to estimate a value of π.Continue reading
This is a simple Python project implementing a function to calculate the factors of a given integer, ie. all of the numbers which divide into that number. The core function returns a list of the factors of the number argument but as a bonus we can use that to write a generator function consisting of just one line of code!Continue reading
In a few of my posts I have used various ANSI terminal codes to manipulate terminal output, specifically moving the cursor around and changing text colours. These codes are often cryptic, can be cumbersome if used extensively, and cannot be relied upon to work across different platforms. A better solution is to use Python's implementation of the venerable curses library, and in this post I will provide a short introduction to what I consider its core functionalities: moving the cursor around and printing in different colours.Continue reading