Posts Tagged 'Recreational Maths'

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.

electricplugs-01

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

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Metallic Means

goldenmean-pentagram

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.

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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.

thatsmathscoverdetail

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.

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Recreational Mathematics is Fun

We all love music, beautiful paintings and great literature without being trained musicians, talented artists or accomplished writers. It is the same with mathematics: we can enjoy the elegance of brilliant logical arguments and appreciate the beauty of mathematical structures and symmetries without being skilled creators of new theorems. [See TM097, or search for “thatsmaths” at irishtimes.com].

HardingGallery

Harding Gallery. Image from Science Museum, London (www.sciencemuseum.org.uk).

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Lateral Thinking in Mathematics

Many problems in mathematics that appear difficult to solve turn out to be remarkably simple when looked at from a new perspective. George Pólya, a Hungarian-born mathematician, wrote a popular book, How to Solve It, in which he discussed the benefits of attacking problems from a variety of angles [see TM094, or search for “thatsmaths” at irishtimes.com].

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Bloom’s attempt to Square the Circle

The quadrature of the circle is one of the great problems posed by the ancient Greeks. This “squaring of the circle” was also an issue of particular interest to Leopold Bloom, the central character in James Joyce’s novel Ulysses, whom we celebrate today, Bloomsday, 16 June 2016 [see TM093, or search for “thatsmaths” at irishtimes.com].

Joyces-Tower

Joyce’s Tower, Sandycove, Co Dublin.

The challenge is to construct a square with area equal to that of a given circle using only the methods of classical geometry. Thus, only a ruler and compass may be used in the construction and the process must terminate in a finite number of steps.

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Mathematics Everywhere (in Blackrock Station)

Mathematics is everywhere. We are often unaware of it but, when we observe our environment consciously, we can see mathematical structures all around us.

Blackrock-Footbridge

This footbridge is a cornucopia of mathematical forms.

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