Anscombe’s Quartet was devised by the statistician Francis Anscombe to illustrate how important it was to not just rely on statistical measures when analyzing data. To do this he created 4 data sets which would produce nearly identical statistical measures. The scatter graphs above generated by the Python code here. Statistical measures 1) Mean of […]

Hailstone Numbers Hailstone numbers are created by the following rules: if n is even: divide by 2 if n is odd: times by 3 and add 1 We can then generate a sequence from any starting number. For example, starting with 10: 10, 5, 16, 8, 4, 2, 1, 4, 2, 1… we can see […]

Chaos and strange Attractors: Henon’s map Henon’s map was created in the 1970s to explore chaotic systems. The general form is created by the iterative formula: The classic case is when a = 1.4 and b = 0.3 i.e: To see how points are generated, let’s choose a point near the origin. If we take […]

The Barnsley Fern: Mathematical Art This pattern of a fern pictured above was generated by a simple iterative program designed by mathematician Michael Barnsely. I downloaded the Python code from the excellent Tutorialspoint and then modified it slightly to run on repl.it. What we are seeing is the result of 40,000 individual points – each plotted […]

Galileo’s Inclined Planes This post is based on the maths and ideas of Hahn’s Calculus in Context – which is probably the best mathematics book I’ve read in 20 years of studying and teaching mathematics. Highly recommended for both students and teachers! Hahn talks us though the mathematics, experiments and thought process of Galileo as […]

Finding focus with Archimedes This post is based on the maths and ideas of Hahn’s Calculus in Context – which is probably the best mathematics book I’ve read in 20 years of studying and teaching mathematics. Highly recommended for both students and teachers! Hard as it is to imagine now, for most of the history […]