Ian Short

Blog

Category: Mathematics

The Code

The three part BBC series The Code about maths begins next Wednesday. Presented by Marcus du Sautoy, and supported by the Open University. We have created some Open University hexagonal shaped cards to accompany the series. They are meant to be drinks mats (think beer mats). I’m worried they will be too thin to be […]

TED Talks

TED is a group in the USA which organises lectures. Here’s a TED lecture about teaching maths: Dan Meyer. Dan argues that you should ask practical maths questions in a bare form. For example, you could ask, “You chuck a 1kg rock upwards at 2 metres per second; how high does it go?” Dan suggests […]

Least integer game

Here is an exercise that can be performed with a group of at least three people. Each person secretly writes down a positive integer. The person with the least positive integer that nobody else has written down wins the game. Everyone is aware of the object of the exercise. There seems to be game theory […]

A seminar by Tom Körner

Tom Körner gave a seminar here at the Open University a couple of weeks back about using the Baire Category Theorem to prove a quantitative form of a theorem of Rudin. Tom made some passing remarks on the Central Limit Theorem, which I discuss and develop in this post. Central Limit Theorem. Let X1, X2,… […]

Graph theory and game theory

Some months ago I discussed the following problem with Steve Hewson and Mike Pearson after an NRICH meeting. Two people play a game with a finite graph. They take turns in colouring the uncoloured vertices of the graph, one vertex at a time. One player colours vertices red, and the other player colours vertices green. […]

How to button as badly as possible

The following problem was suggested by Bernard Murphy at Jenny Piggott’s retirement meeting in Cambridge on Tuesday 13 July. Problem Consider eight jacket buttons in a column, as shown on the left hand side of the image below. We can unbutton the eight buttons in various orders; one such order is shown on the right […]

Candle lighting

How quickly can a number of people, each with an unlit candle, light their candles from a single lit candle? This problem presented itself during a service in St. Mary’s Church in Maynooth, Ireland, to which I was kindly invited on Holy Saturday (3 April 2010). The congregation were seated in a block, and each […]

Dividing walls

Here are some problems I developed for NRICH on disconnecting sets of points. Introduction There is an island, shown below, which contains five towns, each marked by a coloured disc. The people from the red towns are arch rivals with the people from the blue towns, so they decide to build a wall to separate […]

Semi-log graphs

Introduction Last week E asked me about some biological data which could be modelled by an exponential curve, similar to the one shown below. It is the graph of a function such as f(x) = kexp(-sx), for positive constants k and s. Ellie had another version of this graph, shown below. I immediately thought that […]

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