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].

## Posts Tagged 'Recreational Maths'

### Recreational Mathematics is Fun

Published August 18, 2016 Irish Times Leave a CommentTags: Recreational Maths

### Lateral Thinking in Mathematics

Published July 7, 2016 Irish Times Leave a CommentTags: Algorithms, Puzzles, Recreational Maths

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].

### Bloom’s attempt to Square the Circle

Published June 16, 2016 Irish Times Leave a CommentTags: Geometry, Recreational Maths

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].

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.

### Mathematics Everywhere (in Blackrock Station)

Published May 26, 2016 Occasional Leave a CommentTags: Geometry, Recreational Maths

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

Continue reading ‘Mathematics Everywhere (in Blackrock Station)’

### The Imaginary Power Tower: Part II

Published March 31, 2016 Occasional Leave a CommentTags: Analysis, Recreational Maths

This is a continuation of last week’s post: LINK

The complex power tower is defined by an `infinite tower’ of exponents:

The sequence of successive approximations to this function is

If the sequence converges it is easy to solve numerically for a given .

In Part I we described an attempt to fit a logarithmic spiral to the sequence . While the points of the sequence were close to such a curve they did not lie exactly upon it. Therefore, we now examine the asymptotic behaviour of the sequence for large .

### The Imaginary Power Tower: Part I

Published March 24, 2016 Occasional Leave a CommentTags: Analysis, Recreational Maths

The function defined by an `infinite tower’ of exponents,

is called the *Power Tower function*. We consider the sequence of successive approximations to this function:

As , the sequence converges for . This result was first proved by Euler. For an earlier post on the power tower, click here.

### How many Christmas Gifts?

Published December 17, 2015 Irish Times Leave a CommentTags: Number Theory, Recreational Maths

We all know the festive carol *The Twelve Days of Christmas*. Each day, “my true love” receives an increasing number of gifts. On the first day there is one gift, a partridge in a pear tree. On the second, two turtle doves and another partridge, making three. There are six gifts on the third day, ten on the fourth, fifteen on the fifth, and so on.

Here is a Christmas puzzle: what is the total number of gifts over the twelve days? [TM083, or search for “thatsmaths” at irishtimes.com]