Statistics to win penalty shoot-outs With the World Cup upon us again we can perhaps look forward to yet another heroic defeat on penalties by England. England are in fact the worst country of any of the major footballing nations at taking penalties, having won only 1 out of 7 shoot-outs at the Euros and […]

This carries on the previous investigation into Farey sequences, and is again based on the current Nrich task Ford Circles. Below are the Farey sequences for F2, F3 and F4. You can read about Farey sequences in the previous post. This time I’m going to explore the link between Farey sequences and circles. First we […]

Modelling more Chaos This post was inspired by Rachel Thomas’ Nrich article on the same topic. I’ll carry on the investigation suggested in the article. We’re going to explore chaotic behavior – where small changes to initial conditions lead to widely different outcomes. Chaotic behavior is what makes modelling (say) weather patterns so complex. f(x) […]

This is a mini investigation based on the current Nrich task Farey Sequences. As Nrich explains: I’m going to look at Farey sequences (though I won’t worry about rearranging them in order of size). Here are some of the first Farey sequences. The missing fractions are all ones which simplify to a fraction already on […]

Modelling Chaos This post was inspired by Rachel Thomas’ Nrich article on the same topic. I’ll carry on the investigation suggested in the article. We’re going to explore chaotic behavior – where small changes to initial conditions lead to widely different outcomes. Chaotic behavior is what makes modelling (say) weather patterns so complex. Let’s start […]

Modelling tides: What is the effect of a full moon? Let’s have a look at the effect of the moon on the tides in Phuket. The Phuket tide table above shows the height of the tide (meters) on given days in March, with the hours along the top. So if we choose March 1st (full […]