Anyone who lives by the sea is familiar with the regular ebb and flow of the tides. But we all live at the bottom of an ocean of air. The atmosphere, like the ocean, is a fluid envelop surrounding the Earth, and is subject to the influence of the Sun and Moon. While sea tides have been known for more than two thousand years, the discovery of tides in the atmosphere had to await the invention of the barometer [TM202 or search for “thatsmaths” at irishtimes.com].

## Archive for the 'Irish Times' Category

### We are living at the bottom of an ocean

Published January 7, 2021 Irish Times Leave a CommentTags: Geophysics

### Arrangements and Derangements

Published December 24, 2020 Irish Times Leave a CommentTags: Combinatorics, Number Theory

Six students entering an examination hall place their cell-phones in a box. After the exam, they each grab a phone at random as they rush out. What is the likelihood that none of them gets their own phone? The surprising answer — about 37% whatever the number of students — emerges from the theory of derangements.

### On what Weekday is Christmas? Use the Doomsday Rule

Published December 17, 2020 Irish Times Leave a CommentTags: Algorithms

An old nursery rhyme begins “Monday’s child is fair of face / Tuesday’s child is full of grace”. Perhaps character and personality were determined by the weekday of birth. More likely, the rhyme was to help children learn the days of the week. But how can we determine the day on which we were born without the aid of computers or calendars? Is there an algorithm – a recipe or rule – giving the answer? [TM201 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘On what Weekday is Christmas? Use the Doomsday Rule’

### Decorating Christmas Trees with the Four Colour Theorem

Published December 3, 2020 Irish Times Leave a CommentTags: Geometry, Topology

When decorating our Christmas trees, we aim to achieve an aesthetic balance. Let’s suppose that there is a plenitude of baubles, but that their colour range is limited. We could cover the tree with bright shiny balls, but to have two baubles of the same colour touching might be considered garish. How many colours are required to avoid such a catastrophe? [TM200 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Decorating Christmas Trees with the Four Colour Theorem’

### Ireland’s Mapping Grid in Harmony with GPS

Published November 19, 2020 Irish Times Leave a CommentTags: Geophysics, Maps, Spherical Trigonometry

The earthly globe is spherical; more precisely, it is an oblate spheroid, like a ball slightly flattened at the poles. More precisely still, it is a triaxial ellipsoid that closely approximates a “geoid”, a surface of constant gravitational potential [TM199 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Ireland’s Mapping Grid in Harmony with GPS’

### Weather Forecasts get Better and Better

Published November 5, 2020 Irish Times Leave a CommentTags: Geophysics, Numerical Weather Prediction

Weather forecasts are getting better. Fifty years ago, predictions beyond one day ahead were of dubious utility. Now, forecasts out to a week ahead are generally reliable [TM198 or search for “thatsmaths” at irishtimes.com].

Careful measurements of forecast accuracy have shown that the range for a fixed level of skill has been increasing by one day every decade. Thus, today’s one-week forecasts are about as good as a typical three-day forecast was in 1980. How has this happened? And will this remarkable progress continue?### Terence Tao to deliver the Hamilton Lecture

Published October 15, 2020 Irish Times Leave a CommentTags: Hamilton

Pick a number; if it is even, divide it by 2; if odd, triple it and add 1. Now repeat the process, each time halving or else tripling and adding 1. Here is a surprise: no matter what number you pick, you will eventually arrive at 1. Let’s try 6: it is even, so we halve it to get 3, which is odd so we triple and add 1 to get 10. Thereafter, we have 5, 16, 8, 4, 2 and 1. From then on, the value cycles from 1 to 4 to 2 and back to 1 again, forever. Numerical checks have shown that all numbers up to one hundred million million million reach the 1–4–2–1 cycle [TM197 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Terence Tao to deliver the Hamilton Lecture’

### Mathematics and the Nature of Physical Reality

Published October 1, 2020 Irish Times 1 CommentTags: Logic, Philosophy

Applied mathematics is the use of maths to address questions and solve problems outside maths itself. Counting money, designing rockets and vaccines, analysing internet traffic and predicting the weather all involve maths. But why does this work? Why is maths so successful in describing physical reality? How is it that the world can be understood mathematically? [TM196, or search for “thatsmaths” at irishtimes.com]. Continue reading ‘Mathematics and the Nature of Physical Reality’

### Will mathematicians be replaced by computers?

Published September 17, 2020 Irish Times Leave a CommentTags: Computer Science

There are ongoing rapid advances in the power and versatility of AI or artificial intelligence. Computers are now producing results in several fields that are far beyond human capability. The trend is unstoppable, and is having profound effects in many areas of our lives. Will mathematicians be replaced by computers? [TM195 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Will mathematicians be replaced by computers?’

### Suitable Names for Large Numbers

Published September 3, 2020 Irish Times Leave a CommentTags: Arithmetic

One year ago, there were just two centibillionaires, Jeff Bezos and Bill Gates. Recently, Facebook’s Mark Zuckerberg has joined the Amazon and Microsoft founders. Elon Musk, CEO of Tesla and SpaceX, is tipped to be next to join this exclusive club [TM194 or search for “thatsmaths” at irishtimes.com].

### Is There Anyone Out There? The Drake Equation gives a Clue

Published August 20, 2020 Irish Times Leave a CommentTags: Astronomy

The Drake Equation is a formula for the number of developed civilizations in our galaxy, the Milky Way. This number is determined by seven factors. Some are known with good accuracy but the values of most are quite uncertain. It is a simple equation comprising seven terms multiplied together [TM193 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Is There Anyone Out There? The Drake Equation gives a Clue’

### Cornelius Lanczos – Inspired by Hamilton’s Quaternions

Published July 16, 2020 Irish Times Leave a CommentTags: Analysis, Applied Maths, Mechanics, Relativity

In May 1954, Cornelius Lanczos took up a position as senior professor in the School of Theoretical Physics at the Dublin Institute for Advanced Studies (DIAS). The institute had been established in 1940 by Eamon de Valera, with a School of Theoretical Physics and a School of Celtic Studies, reflecting de Valera’s keen interest in mathematics and in the Irish language. Later, a School of Cosmic Physics was added. DIAS remains a significant international centre of research today [TM191 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Cornelius Lanczos – Inspired by Hamilton’s Quaternions’

### The Ever-growing Goals of Googology

Published July 2, 2020 Irish Times Leave a CommentTags: Arithmetic, Number Theory

In 1920, a kindergarten class was asked to describe the biggest number that they could imagine. One child proposed to “write down digits until you get tired”. A more concrete idea was to write a one followed by 100 zeros. This number, which scientists would express as ten to the power 100, was given the name “googol” by its inventor [TM190; or search for “thatsmaths” at irishtimes.com ].

### The Geography of Europe is Mapped in our Genes

Published June 18, 2020 Irish Times Leave a CommentTags: biology

It may seem too much to expect that a person’s geographic origin can be determined from a DNA sample. But, thanks to a mathematical technique called principal component analysis, this can be done with remarkable accuracy. It works by reducing multi-dimensional data sets to just a few variables [TM189; or search for “thatsmaths” at irishtimes.com ].

Continue reading ‘The Geography of Europe is Mapped in our Genes’

### Pooling Expertise to Tackle Covid-19

Published June 4, 2020 Irish Times Leave a CommentTags: Applied Maths, Epidemiology

Our lives have been severely restricted in recent months. We are assured that the constraints have been imposed following “the best scientific advice”, but what is the nature of this advice? Among the most important scientific tools used for guidance on the Covid-19 outbreak are mathematical models [TM188; or search for “thatsmaths” at irishtimes.com ].

### Changing the way that we look at the world

Published May 21, 2020 Irish Times Leave a CommentTags: Geometry

Albrecht Dürer was born in Nuremberg in 1471, third of a family of eighteen children. Were he still living, he would be celebrating his 549th birthday today. Dürer’s artistic genius was clear from an early age, as evidenced by a self-portrait he painted when just thirteen [TM187; or search for “thatsmaths” at irishtimes.com ].

In 1494, Dürer visited Italy, where he travelled for a year. A novel connection between art and mathematics was emerging around that time. By using rules of perspective, artists could represent objects in three-dimensional space on a plane canvas with striking realism. Dürer was convinced that “the new art must be based upon science; in particular, upon mathematics, as the most exact, logical, and graphically constructive of the sciences”*.*

Continue reading ‘Changing the way that we look at the world’

### John Casey: a Founder of Modern Geometry

Published May 7, 2020 Irish Times Leave a CommentTags: Geometry, Ireland

Next Tuesday – 12th May – is the 200^{th} anniversary of the birth of John Casey, a notable Irish geometer. Casey was born in 1820 in Kilbeheny, Co Limerick. He was educated in nearby Mitchelstown, where he showed great aptitude for mathematics and also had a gift for languages. He became a mathematics teacher, first in Tipperary Town and later in Kilkenny [TM186; or search for “thatsmaths” at irishtimes.com ].

### Exponential Growth must come to an End

Published April 16, 2020 Irish Times Leave a CommentTags: Analysis, Applied Maths

In its initial stages, the Covid-19 pandemic grew at an exponential rate. What does this mean? The number of infected people in a country is growing exponentially if it increases by a fixed multiple R each day: if N people are infected today, then R times N are infected tomorrow. The size of the growth-rate R determines how rapidly the virus is spreading. An example should make this clear [TM185 or search for “thatsmaths” at irishtimes.com].

### The Mathematics of Fair Play in Video Games

Published April 2, 2020 Irish Times Leave a CommentTags: Algorithms, Games, Hamilton

Video games generate worldwide annual sales of about $150 billion. With millions of people confined at home with time to spare, the current pandemic may benefit the industry. At the core of a video game is a computer program capable of simulating a range of phenomena in the real world or in a fantasy universe, of generating realistic imagery and of responding to the actions and reactions of the players. At every level, mathematics is crucial [TM184 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The Mathematics of Fair Play in Video Games’

### Covid-19: Modelling the evolution of a viral outbreak

Published March 19, 2020 Irish Times Leave a CommentTags: Epidemiology

There is widespread anxiety about the threat of the Covid-19 virus. Mathematics now plays a vital role in combating the spread of epidemics, and will help us to bring this outbreak under control. For centuries, mathematics has been used to solve problems in astronomy, physics and engineering. But now biology and medicine have become topics of mathematical investigation, and applications in these areas are certain to expand in the future [TM183 or search for “thatsmaths” at irishtimes.com].

How rapidly will the viral infection spread? How long will it remain a problem? When will it reach a peak and how quickly will it die out? Most important, what effective steps can we can take to control the outbreak and to minimize the damage caused? When vaccines become available, what is the optimal strategy for their use? Models provide valuable evidence for decision makers.

Continue reading ‘Covid-19: Modelling the evolution of a viral outbreak’

### Samuel Haughton and the Humane Drop

Published March 5, 2020 Irish Times Leave a CommentTags: Applied Maths, History

Samuel Haughton was born in Co. Carlow in 1821. He entered Trinity College Dublin aged just sixteen and graduated in 1843. He was elected a fellow in 1844 and was appointed professor of geology in 1851. He took up the study of medicine and graduated as a Doctor of Medicine in 1862, aged 40 [TM182 or search for “thatsmaths” at irishtimes.com].

In addition to his expertise in geology and medicine, Haughton was a highly talented applied mathematician. His mathematical investigations included the study of the motion of solid and fluid bodies, solar radiation, climatology, animal mechanics and ocean tides. One of his more bizarre applications of mathematics was to demonstrate a humane method of execution by hanging, by lengthening the drop to ensure instant death.

### How many numbers begin with a 1? More than 30%!

Published February 20, 2020 Irish Times Leave a CommentTags: Probability, Statistics

The irregular distribution of the first digits of numbers in data-bases provides a valuable tool for fraud detection. A remarkable rule that applies to many datasets was accidentally discovered by an American physicist, Frank Benford, who described his discovery in a 1938 paper, “The Law of Anomalous Numbers” [TM181 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘How many numbers begin with a 1? More than 30%!’

### Using Maths to Reduce Aircraft Noise

Published February 6, 2020 Irish Times Leave a CommentTags: Fluid Dynamics, modelling

If you have ever tried to sleep under a flight-path near an airport, you will know how serious the problem of aircraft noise can be. Aircraft noise is amongst the loudest sounds produced by human activities. The noise is over a broad range of frequencies, extending well beyond the range of hearing. The problem of aviation noise has become more severe as aircraft engines have become more powerful [TM180 or search for “thatsmaths” at irishtimes.com].

### The “extraordinary talent and superior genius” of Sophie Germain

Published January 16, 2020 Irish Times Leave a CommentTags: History, Mechanics, Number Theory

When a guitar string is plucked, we don’t see waves travelling along the string. This is because the ends are fixed. Instead, we see a standing-wave pattern. Standing waves are also found on drum-heads and on the sound-boxes of violins. The shape of a violin strongly affects the quality and purity of the sound, as it determines the mixture of standing wave harmonics that it can sustain [TM179 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The “extraordinary talent and superior genius” of Sophie Germain’

### The knotty problem of packing DNA

Published January 2, 2020 Irish Times Leave a CommentTags: biology, Topology

Soon it will be time to pack away the fairy lights. If you wish to avoid the knotty task of disentangling them next December, don’t just throw them in a box; roll them carefully around a stout stick or a paper tube. Any long and flexible string or cable, squeezed into a confined volume, is likely to become entangled: just think of garden hoses or the wires of headphones [TM178 or search for “thatsmaths” at irishtimes.com].

### Having your Christmas Cake and Eating it

Published December 19, 2019 Irish Times Leave a CommentTags: Algorithms

As Christmas approaches, the question of fair sharing comes into focus. Readers can rejoice that there has been a recent breakthrough in cake-cutting theory. Cake cutting may sound limited, but it is important for many practical problems. A cake is a metaphor for a parcel of land to be divided, broadcast frequencies to be allocated, divorce settlements, chores to be done by flatmates, border resolutions or any other valuable or scarce resource to be shared [TM177 or search for “thatsmaths” at irishtimes.com].

### A New Mathematical Discovery from Neutrino Physics

Published December 5, 2019 Irish Times Leave a CommentTags: Physics

Although abstract in character, mathematics has concrete origins: the greatest advances have been inspired by the natural world. Recently, a new result in linear algebra was discovered by three physicists trying to understand the behaviour of neutrinos [TM176 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘A New Mathematical Discovery from Neutrino Physics’

### Airport Baggage Screening with X-Ray Tomography

Published November 21, 2019 Irish Times Leave a CommentTags: Algorithms

When you check in your baggage for a flight, it must be screened before it is allowed on the plane. Baggage screening detects threats within luggage and personal belongings by x-ray analysis as they pass along a conveyor belt. Hold-baggage and passenger screening systems are capable of detecting contraband materials, narcotics, explosives and weapons [TM175 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Airport Baggage Screening with X-Ray Tomography’

### The Vastness of Mathematics: No One Knows it All

Published November 7, 2019 Irish Times Leave a CommentTags: Education, History

No one person can have mastery of the entirety of mathematics. The subject has become so vast that the best that can be achieved is a general understanding and appreciation of the main branches together with expertise in one or two areas [TM174 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The Vastness of Mathematics: No One Knows it All’

### Maths and Poetry: Beauty is the Link

Published October 17, 2019 Irish Times Leave a CommentTags: Hamilton

Mathematicians are not renowned for their ability to reach the deepest recesses of the human soul. This talent is usually associated with great artists and musicians, and a good poet can move us profoundly with a few well-chosen words [TM173 or search for “thatsmaths” at irishtimes.com].

### Emergence of Complex Behaviour from Simple Roots

Published October 3, 2019 Irish Times Leave a CommentTags: Algorithms, biology, Computer Science

It is exhilarating to watch a large flock of birds swarming in ever-changing patterns. Swarming is an emergent behaviour, resulting from a set of simple rules followed by each individual animal, bird or fish, without any centralized control or leadership.

Continue reading ‘Emergence of Complex Behaviour from Simple Roots’

### George Salmon, Mathematician & Theologian

Published September 19, 2019 Irish Times Leave a CommentTags: History

As you pass through the main entrance of Trinity College, the iconic campanile stands before you, flanked, in pleasing symmetry, by two life-size statues. On the right, on a granite plinth is the historian and essayist William Lecky. On the left, George Salmon (1819–1904) sits on a limestone platform.

Salmon was a distinguished mathematician and theologian and Provost of Trinity College. For decades, the two scholars have gazed down upon multitudes of students crossing Front Square. The life-size statue of Salmon, carved from Galway marble by the celebrated Irish sculptor John Hughes, was erected in 1911. Next Wednesday will be the 200^{th} anniversary of Salmon’s birth [TM171 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘George Salmon, Mathematician & Theologian’

### An English Lady with a Certain Taste

Published September 5, 2019 Irish Times Leave a CommentTags: Statistics

One hundred years ago, an English lady, Dr Muriel Bristol, amazed some leading statisticians by proving that she could determine by taste the order in which the constituents are poured in a cup of tea. One of the statisticians was Ronald Fisher. The other was William Roach, who was to marry Dr Bristol shortly afterwards.

Many decisions in medicine, economics and other fields depend on carefully designed experiments. For example, before a new treatment is proposed, its efficacy must be established by a series of rigorous tests. Everyone is different, and no one course of treatment is necessarily best in all cases. Statistical evaluation of data is an essential part of the evaluation of new drugs [TM170 or search for “thatsmaths” at irishtimes.com].

### The Brief and Tragic Life of Évariste Galois

Published August 15, 2019 Irish Times Leave a CommentTags: Algebra, Group Theory, History

On the morning of 30 May 1832 a young man stood twenty-five paces from his friend. Both men fired, but only one pistol was loaded. Évariste Galois, a twenty year old mathematical genius, fell to the ground. The cause of Galois’s death is veiled in mystery and speculation. Whether both men loved the same woman or had irreconcilable political differences is unclear. But Galois was abandoned, mortally wounded, on the duelling ground at Gentilly, just south of Paris. By noon the next day he was dead [TM169 or search for “Galois” at irishtimes.com].

Continue reading ‘The Brief and Tragic Life of Évariste Galois’

### Stokes’s 200th Birthday Anniversary

Published August 8, 2019 Irish Times Leave a CommentTags: Fluid Dynamics, History, Physics

Next Tuesday, the 30th of August, is the 200th anniversary of the birth of George Gabriel Stokes. This extended blog post is to mark that occasion. See also an article in The Irish Times.

### Algorithms: Recipes for Success

Published August 1, 2019 Irish Times Leave a CommentTags: Algorithms, Computer Science

The impact of computing on society is ever-increasing. Web-based commerce continues to grow and artificial intelligence now pervades our lives. To make wise choices, we need to understand how computers operate and how we can deploy them most constructively. Listen to any computer scientist and soon you will hear the word “algorithm” [TM168 or search for “thatsmaths” at irishtimes.com].

### Learning Maths without even Trying

Published July 18, 2019 Irish Times Leave a CommentTags: 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].

### What did the Romans ever do for Maths?

Published July 4, 2019 Irish Times 1 CommentTags: Arithmetic, History

The ancient Romans developed many new techniques for engineering and architecture. The citizens of Rome enjoyed fountains, public baths, central heating, underground sewage systems and public toilets. All right, but apart from sanitation, medicine, education, irrigation, roads and aqueducts, what did the Romans ever do for maths? [TM166 or search for “thatsmaths” at irishtimes.com].

### Simple Curves that Perplex Mathematicians and Inspire Artists

Published June 20, 2019 Irish Times Leave a CommentTags: Algorithms, Topology

The preoccupations of mathematicians can seem curious and strange to *normal* people. They sometimes expend great energy proving results that appear glaringly obvious. One such result is called the **Jordan** **Curve** **Theorem**. We all know that a circle has an inside and an outside, and that this property also holds for a much larger collection of closed curves [TM165 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Simple Curves that Perplex Mathematicians and Inspire Artists’

### Spin-off Effects of the Turning Earth

Published June 6, 2019 Irish Times Leave a CommentTags: Fluid Dynamics, Geophysics, Numerical Weather Prediction

On the rotating Earth, a moving object deviates from a straight line, being deflected to the right in the northern hemisphere and to the left in the southern hemisphere. The deflecting force is named after a nineteenth century French engineer, Gaspard-Gustave de Coriolis [TM164 or search for “thatsmaths” at irishtimes.com].

Coriolis was interested in the dynamics of machines, such as water mills, with rotating elements. He was not concerned with the turning Earth or the oceans and atmosphere surrounding it. But it is these fluid envelopes of the planet that are most profoundly affected by the Coriolis force.

### The Rise and Rise of Women in Mathematics

Published May 16, 2019 Irish Times Leave a CommentTags: History, Social attitudes

The influential collection of biographical essays by Eric Temple Bell, *Men of Mathematics,* was published in 1937. It covered the lives of about forty mathematicians, from ancient times to the beginning of the twentieth century. The book inspired many boys to become mathematicians. However, it seems unlikely that it inspired many girls: the only woman to get more than a passing mention was Sofia Kovalevskaya, a brilliant Russian mathematician and the first woman to obtain a doctorate in mathematics [TM163 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The Rise and Rise of Women in Mathematics’

### Kepler’s Vanishing Circles Hidden in Hamilton’s Hodograph

Published May 2, 2019 Irish Times Leave a CommentTags: Astronomy, Hamilton, Mechanics

The Greeks regarded the heavens as the epitome of perfection. All flaws and blemishes were confined to the terrestrial domain. Since the circle is perfect in its infinite symmetry, it was concluded by Aristotle that the Sun and planets move in circles around the Earth. Later, the astronomer Ptolemy accounted for deviations by means of additional circles, or epicycles. He stuck with the circular model [TM162 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Kepler’s Vanishing Circles Hidden in Hamilton’s Hodograph’

### Closing the Gap between Prime Numbers

Published April 18, 2019 Irish Times Leave a CommentTags: Arithmetic, Number Theory

Occasionally, a major mathematical discovery comes from an individual working in isolation, and this gives rise to great surprise. Such an advance was announced by Yitang Zhang six years ago. [TM161 or search for “thatsmaths” at irishtimes.com].

### A Pioneer of Climate Modelling and Prediction

Published April 4, 2019 Irish Times Leave a CommentTags: Climate Modelling, Numerical Weather Prediction

Today we benefit greatly from accurate weather forecasts. These are the outcome of a long struggle to advance the science of meteorology. One of the major contributors to that advancement was Norman A. Phillips, who died in mid-March, aged 95. Phillips was the first person to show, using a simple computer model, that mathematical simulation of the Earth’s climate was practicable [TM160 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘A Pioneer of Climate Modelling and Prediction’

### Joseph Fourier and the Greenhouse Effect

Published March 21, 2019 Irish Times Leave a CommentTags: Applied Maths, Fourier analysis, Geophysics

Jean-Baptiste Joseph Fourier, French mathematician and physicist, was born in Auxerre 251 years ago today. He is best known for the mathematical techniques that he developed in his analytical theory of heat transfer. Over the past two centuries, his methods have evolved into a major subject, harmonic analysis, with widespread applications in number theory, signal processing, quantum mechanics, weather prediction and a broad range of other fields [TM159 or search for “thatsmaths” at irishtimes.com].

### Hokusai’s Great Wave and Roguish Behaviour

Published March 7, 2019 Irish Times Leave a CommentTags: Wave Motion

“The Great Wave off Kanagawa”, one of the most iconic works of Japanese art, shows a huge breaking wave with foam thrusting forward at its crest, towering over three fishing boats, with Mt Fuji in the background [TM158 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Hokusai’s Great Wave and Roguish Behaviour’

### Multiple Discoveries of the Thue-Morse Sequence

Published February 21, 2019 Irish Times Leave a CommentTags: Algorithms, Number Theory

It is common practice in science to name important advances after the first discoverer or inventor. However, this process often goes awry. A humorous principle called Stigler’s Law holds that no scientific result is named after its original discoverer. This law was formulated by Professor Stephen Stigler of the University of Chicago in his publication “Stigler’s law of eponymy”. He pointed out that his “law” had been proposed by others before him so it was, in a sense, self-verifying. [TM157 or search for “thatsmaths” at irishtimes.com].

Continue reading ‘Multiple Discoveries of the Thue-Morse Sequence’### Rambling and Reckoning

Published February 7, 2019 Irish Times Leave a CommentTags: 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’### Discoveries by Amateurs and Distractions by Cranks

Published January 17, 2019 Irish Times Leave a CommentTags: 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’

### Trappist-1 & the Age of Aquarius

Published January 3, 2019 Irish Times Leave a CommentTags: Astronomy, Mechanics

The Pythagoreans believed that the planets generate sounds as they move through the cosmos. The idea of the harmony of the spheres was brought to a high level by Johannes Kepler in his book *Harmonices Mundi*, where he identified many simple relationships between the orbital periods of the planets [TM154 or search for “thatsmaths” at irishtimes.com].

Kepler’s idea was not much supported by his contemporaries, but in recent times astronomers have come to realize that resonances amongst the orbits has a crucial dynamical function. Continue reading ‘Trappist-1 & the Age of Aquarius’