A Stochastic Estimation of Pi

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.

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Factorization

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!

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An Introduction to curses

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.

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SI Prefixes

Most people are familiar with a few of the more common prefixes used before many units to denote a fraction or a multiple of the unit - kilograms, megabytes, centimetres etc.. As well as these there a number of less well known ones, going right up to yotta and right down to yocto.

As a simple but hopefully enlightening programming exercise I have put together this short Python program to list all the prefixes along with their corresponding powers and multipliers.

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The Caesar Shift Cypher

The Caesar Shift Cypher was named after Julius Caesar and is the simplest method of encypherment possible. It consists of shifting letters along by one or more places, so for example if you use a shift of 1 then A becomes B, B becomes C etc.. To decypher the message you just shift letters in the opposite direction. Clearly it lacks sophistication and can easily be cracked, either by trial and error or, if you have a reasonable length of encrypted text, using frequency analysis.

As a little programming exercise I will code the Caesar Shift Cypher in Python, and in a future post will break it with frequency analysis.

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