Hula hoops were all the rage in 1958. Yo-yos, popular before World War II, were relaunched in the 1960s. Rubik’s Cube, invented in 1974, quickly became a global craze. Sudoku, which had been around for years, was wildly popular when it started to appear in American and European newspapers in 2004.

## Posts Tagged 'Recreational Maths'

### Why Waffle when One Wordle Do?

Published February 24, 2022 Occasional ClosedTags: Algorithms, Recreational Maths

### John Horton Conway: a Charismatic Genius

Published April 23, 2020 Occasional ClosedTags: Games, Group Theory, Number Theory, Recreational Maths, Topology

John Horton Conway was a charismatic character, something of a performer, always entertaining his fellow-mathematicians with clever magic tricks, memory feats and brilliant mathematics. A Liverpudlian, interested from early childhood in mathematics, he studied at Gonville & Caius College in Cambridge, earning a BA in 1959. He obtained his PhD five years later, after which he was appointed Lecturer in Pure Mathematics.

In 1986, Conway moved to Princeton University, where he was Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics. He was awarded numerous honours during his career. Conway enjoyed emeritus status from 2013 until his death just two weeks ago on 11 April.

### Spiralling Primes

Published September 12, 2019 Occasional ClosedTags: Number Theory, Recreational Maths

The prime numbers have presented mathematicians with some of their most challenging problems. They continue to play a central role in number theory, and many key questions remain unsolved.

** Order and Chaos **

The primes have many intriguing properties. In his article “The first 50 million prime numbers”, Don Zagier noted two contradictory characteristics of the distribution of prime numbers. The first is the erratic and seemingly chaotic way in which the primes “grow like weeds among the natural numbers”. The second is that, when they are viewed in the large, they exhibit “stunning regularity”.

### Learning Maths without even Trying

Published July 18, 2019 Irish Times ClosedTags: Education, Ireland, Recreational Maths

Children have an almost limitless capacity to absorb knowledge if it is presented in an appealing and entertaining manner. Mathematics can be daunting, but it is possible to convey key ideas visually so that they are instantly accessible. Visiting Explorium recently, I saw such a visual display demonstrating the theorem of Pythagoras, which, according to Jacob Bronowski, “remains the most important single theorem in the whole of mathematics” [TM167 or search for “thatsmaths” at irishtimes.com].

### Rambling and Reckoning

Published February 7, 2019 Irish Times ClosedTags: Arithmetic, Recreational Maths

A walk on the beach, in the hills or along a river bank provides great opportunities for mathematical reflection. How high is the mountain? How many grains of sand are on the beach? How much water is flowing in the river? [TM156 or search for “thatsmaths” at irishtimes.com].

While the exact answers may be elusive, we can make reasonable guesstimates using basic knowledge and simple mathematical reasoning. And we will be walking in the footsteps of some of the world’s greatest thinkers.

Continue reading ‘Rambling and Reckoning’A Colloquium on Recreational Mathematics took place in Lisbon this week. The meeting, RMC-VI (G4GEurope), a great success, was organised by the Ludus Association, with support from several other agencies: MUHNAC, ULisboa, CMAF-IO, CIUHCT, CEMAPRE, and FCT. It was the third meeting integrated in the Gathering for Gardner movement, which celebrates the great populariser of maths, Martin Gardner. For more information about the meeting, see http://ludicum.org/ev/rm/19 .

Continue reading ‘Our Dearest Problems’### Discoveries by Amateurs and Distractions by Cranks

Published January 17, 2019 Irish Times ClosedTags: History, Ramanujan, Recreational Maths

Do amateurs ever solve outstanding mathematical problems? Professional mathematicians are aware that almost every new idea they have about a mathematical problem has already occurred to others. Any really new idea must have some feature that explains why no one has thought of it before [TM155 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Discoveries by Amateurs and Distractions by Cranks’

### Tom Lehrer: Comical Musical Mathematical Genius

Published September 20, 2018 Irish Times ClosedTags: Education, Music, Recreational Maths

Tom Lehrer, mathematician, singer, songwriter and satirist, was born in New York ninety years ago. He was active in public performance for about 25 years from 1945 to 1970. He is most renowned for his hilarious satirical songs, many of which he recorded and which are available today on YouTube [see TM147, or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Tom Lehrer: Comical Musical Mathematical Genius’

### Kaprekar’s Number 6174

Published January 25, 2018 Occasional ClosedTags: Number Theory, Recreational Maths

The Indian mathematician D. R. Kaprekar spent many happy hours during his youth solving mathematical puzzles. He graduated from Fergusson College in Pune in 1929 and became a mathematical teacher at a school in Devlali, north-east of Mumbai.

### Learning Maths has never been Easier

Published October 19, 2017 Irish Times ClosedTags: Education, Ireland, Recreational Maths

Maths is hard: many people find it inscrutable and have negative attitudes towards maths. They may have bad memories of school maths or have been told they lack mathematical talents. This is unfortunate: we all have the capacity to apply reasoning and logic and we can all do maths. Given the vital role mathematics plays in modern society, there is an urgent need to help young people to become more numerate and comfortable with mathematics. With a wealth of online resources, learning maths has never been easier. [TM125 or search for “thatsmaths” at irishtimes.com].

### Fractions of Fractions of Fractions

Published August 10, 2017 Occasional ClosedTags: Arithmetic, Number Theory, Recreational Maths

Numbers can be expressed in several different ways. We are familiar with whole numbers, fractions and decimals. But there is a wide range of other forms, and we examine one of them in this article. Every rational number can be expanded as a continued fraction:

where all are integers, all positive except perhaps . If we add it to ; then the expansion is unique.

### Patterns in Poetry, Music and Morse Code

Published June 29, 2017 Occasional ClosedTags: Arithmetic, History, Recreational Maths

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.

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?

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?

* * *

### Torricelli’s Trumpet & the Painter’s Paradox

Published April 13, 2017 Occasional ClosedTags: Analysis, Geometry, Recreational Maths

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 for is rotated in 3-space about the x-axis.

Continue reading ‘Torricelli’s Trumpet & the Painter’s Paradox’

### Numerical Coincidences

Published March 23, 2017 Occasional ClosedTags: Number Theory, Recreational Maths

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.

### Topology in the Oval Office

Published February 23, 2017 Occasional ClosedTags: Graph Theory, Recreational Maths, Topology

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.**

### Metallic Means

Published February 9, 2017 Occasional ClosedTags: Algebra, Arithmetic, Recreational Maths

with the value

.

There is no doubt that 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.

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.

### Recreational Mathematics is Fun

Published August 18, 2016 Irish Times ClosedTags: Recreational Maths

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].

### Lateral Thinking in Mathematics

Published July 7, 2016 Irish Times ClosedTags: 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 ClosedTags: 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 ClosedTags: 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 ClosedTags: 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 ClosedTags: 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 ClosedTags: 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]

Suppose six friends visit a pizzeria and have enough cash for just one big pizza. They need to divide it fairly into six equal pieces. That is simple: cut the pizza in the usual way into six equal sectors.

But suppose there is meat in the centre of the pizza and some of the friends are vegetarians. How can we cut the pizza into slices of identical shape and size, some of them not including the central region?

Have a think about this before reading on. There is more than one solution.### Golden Moments

Published March 26, 2015 Occasional ClosedTags: Recreational Maths, Time measurement

Suppose a circle is divided by two radii and the two arcs *a* and *b* are in the golden ratio:

*b* / *a* = ( *a + b *) / *b* = *φ* ≈ 1.618

Then the smaller angle formed by the radii is called the golden angle. It is equal to about 137.5° or 2.4 radians. We will denote the golden angle by *γ*. Its exact value, as a fraction of a complete circle, is ( 3 – √5 ) / 2 ≈ 0.382 cycles.

### Triangular Numbers: EYPHKA

Published October 9, 2014 Occasional ClosedTags: Gauss, Number Theory, Recreational Maths

The maths teacher was at his wits’ end. To get some respite, he set the class a task:

*Add up the first one hundred numbers.*

“That should keep them busy for a while”, he thought. Almost at once, a boy raised his hand and called out the answer. The boy was Carl Friedrich Gauss, later dubbed the Prince of Mathematicians. Continue reading ‘Triangular Numbers: EYPHKA’

### Cartoon Curves

Published September 11, 2014 Occasional ClosedTags: Algebra, Computer Science, Geometry, Recreational Maths

The powerful and versatile computational software program called Mathematica is widely used in science, engineering and mathematics. There is a related system called Wolfram Alpha, a computational knowledge engine, that can do Mathematica calculations and that runs on an iPad.

### Biscuits, Books, Coins and Cards: Massive Hangovers

Published June 12, 2014 Occasional ClosedTags: Arithmetic, Games, Recreational Maths

Have you ever tried to build a high stack of coins? In theory it’s fine: as long as the centre of mass of the coins above each level remains over the next coin, the stack should stand. But as the height grows, it becomes increasingly trickier to avoid collapse.

In theory it is possible to achieve an arbitrarily large hangover — most students find this out for themselves! In practice, at more than about one coin diameter it starts to become difficult to maintain balance.

Continue reading ‘Biscuits, Books, Coins and Cards: Massive Hangovers’

### The High-Power Hypar

Published May 29, 2014 Occasional ClosedTags: Algebra, Gauss, Geometry, Recreational Maths

Maths frequently shows us surprising and illuminating connections between physical systems that are not obviously related: the analysis of one system often turns out to be ideally suited for describing another. To illustrate this, we will show how a surface in three dimensional space — the hyperbolic paraboloid, or *hypar* — pops up in unexpected ways and in many different contexts.

### The Watermelon Puzzle

Published November 14, 2013 Occasional ClosedTags: Algebra, Puzzles, Recreational Maths

An amusing puzzle appears in a recent book by John A. Adam (2013). The answer is very surprising. The book argues in terms of simultaneous equations. A simpler argument, using the diagram below, should make all clear. Continue reading ‘The Watermelon Puzzle’

### New Estimate of the Speed of Light

Published September 12, 2013 Occasional ClosedTags: Mechanics, Physics, Recreational Maths

A team of German scientists have recently discovered a new method of measuring the speed of light using Einstein’s famous equation

*E* = *m c*^{2}

### Amazing Normal Numbers

Published June 21, 2013 Occasional ClosedTags: Number Theory, Recreational Maths

For any randomly chosen decimal number, we might expect that all the digits, 0, 1 , … , 9, occur with equal frequency. Likewise, digit pairs such as 21 or 59 or 83 should all be equally likely to crop up. Similarly for triplets of digits. Indeed, the probability of finding any finite string of digits should depend only on its length. And, sooner or later, we should find any string. That’s “normal”!

Continue reading ‘Amazing Normal Numbers’

With Bloomsday looming, it is time to re-Joyce. We reflect on some properties of a large number occurring in *Ulysses*.

Continue reading ‘Joyce’s Number’

### Chess Harmony

Published January 30, 2013 Occasional ClosedTags: Games, Number Theory, Puzzles, Recreational Maths

Long ago in the Gupta Empire, a great-but-greedy mathematician, Grababundel, presented to the Maharaja a new game that he had devised, called Chaturanga.

Thirty-two of the Maharaja’s subjects, sixteen dressed in white and sixteen in black, were assembled on a field divided into 64 squares. There were rajas and ranis, mahouts and magi, fortiers and foot-soldiers. Continue reading ‘Chess Harmony’

Look at the function defined by an `infinite tower’ of exponents:

It would seem that for *x*>1 this must blow up. But, amazingly, this is not so.

In fact, the function has finite values for positive *x* up to . We call this function the *power tower function*. Continue reading ‘The Power Tower’