Posts Tagged 'Recreational Maths'

Patterns in Poetry, Music and Morse Code

Suppose we have to ascent a flight of stairs and can take only one or two steps at a time. How many different patterns of ascent are there? We start with the simplest cases. With one step there is only one way; with two, there are two: take two single steps or one double step. With three steps, there are three possibilities. We can now proceed in an inductive manner.

The Beer Mat Game

Alice and Bob, are enjoying a drink together. Sitting in a bar-room, they take turns placing beer mats on the table. The only rules of the game are that the mats must not overlap or overhang the edge of the table. The winner is the player who puts down the final mat. Is there a winning strategy for Alice or for Bob?

Image from Flickr.

We start with the simple case of a circular table and circular mats. In this case, there is a winning strategy for the first player. Before reading on, can you see what it is?

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Torricelli’s Trumpet & the Painter’s Paradox

Torricelli’s Trumpet

Evangelista Torricelli, a student of Galileo, is remembered as the inventor of the barometer. He was also a talented mathematician and he discovered the remarkable properties of a simple geometric surface, now often called Torricelli’s Trumpet. It is the surface generated when the curve ${y=1/x}$ for ${x\ge1}$ is rotated in 3-space about the x-axis.

Numerical Coincidences

A numerical coincidence is an equality or near-equality between different mathematical quantities which has no known theoretical explanation. Sometimes such equalities remain mysterious and intriguing, and sometimes theory advances to the point where they can be explained and are no longer regarded as surprising.

Cosine of 355 radians is almost exactly equal to -1. Is this a coincidence? Read on!

Topology in the Oval Office

Imagine a room – the Oval Office for example – that has three electrical appliances:

•  An air-conditioner ( a ) with an American plug socket ( A ),

•  A boiler ( b ) with a British plug socket ( B ),

•  A coffee-maker ( c ) with a Continental plug socket ( C ).

The problem is to connect each appliance to the correct socket, avoiding any crossings of the connecting wires.

Fig. 1: Positions of appliances and sockets for Problem 1.

Metallic Means

The golden mean occurs repeatedly in the pentagram [image Wikimedia Commons]

Everyone knows about the golden mean. It must be one of the most written-about numbers, certainly in recreational mathematics. It is usually denoted by ${\phi}$ and is the positive root of the quadratic equation

$\displaystyle x^2 - x - 1 = 0 \ \ \ \ \ (1)$

with the value

${\phi = (1+\sqrt{5})/2 \approx 1.618}$.

There is no doubt that ${\phi}$ is significant in many biological contexts and has also been an inspiration for artists. Called the Divine Proportion, it  was described in a book of that name by Luca Pacioli, a contemporary and friend of Leonardo da Vinci.

That’s Maths Book Published

A book of mathematical articles, That’s Maths, has just been published. The collection of 100 articles includes pieces that have appeared in The Irish Times over the past few years, blog posts from this website and a number of articles that have not appeared before.

The book has been published by Gill Books and copies are available through all good booksellers in Ireland, and from major online booksellers. An E-Book is also available online.