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The Geography of Europe is Mapped in our Genes

Published June 18, 2020 Irish Times Closed
Tags: 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 ].

Predicted locations for more than 1200 individuals, based on DNA markers in their genome (figure from Nature).

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Pooling Expertise to Tackle Covid-19

Published June 4, 2020 Irish Times Closed
Tags: 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 ].

Prof Philip Nolan, Chairman of IEMAG (Photograph: Tom Honan

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Changing the way that we look at the world

Published May 21, 2020 Irish Times Closed
Tags: Geometry

Self-portrait by Dürer when aged 26.

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”.

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John Casey: a Founder of Modern Geometry

Published May 7, 2020 Irish Times Closed
Tags: Geometry, Ireland

John Casey (1820-1891).

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 ].

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Exponential Growth must come to an End

Published April 16, 2020 Irish Times Closed
Tags: 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].

“Flattening the curve” [image from ECDC].

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The Mathematics of Fair Play in Video Games

Published April 2, 2020 Irish Times Closed
Tags: 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].

League of Legends, from Riot Games.

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Covid-19: Modelling the evolution of a viral outbreak

Published March 19, 2020 Irish Times Closed
Tags: Epidemiology

The illness is called Covid-19 but the virus is known as SARS-CoV-2 (Severe Acute Respiratory Syndrome coronavirus 2) [Image from US agency Centers for Disease Control and Prevention].

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.

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Samuel Haughton and the Humane Drop

Published March 5, 2020 Irish Times Closed
Tags: Applied Maths, History

Samuel Haughton (1821-1897).

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.

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

Published February 20, 2020 Irish Times Closed
Tags: 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].

Benford-Distribution-3

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Using Maths to Reduce Aircraft Noise

Published February 6, 2020 Irish Times Closed
Tags: 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].

Engine inlet of a CFM56-3 turbofan engine on a Boeing 737-400 [image Wikimedia Commons].

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The “extraordinary talent and superior genius” of Sophie Germain

Published January 16, 2020 Irish Times Closed
Tags: 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].

French postage stamp, issued in 2016, to commemorate the
250th anniversary of the birth of Sophie Germain (1776-1831).

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The knotty problem of packing DNA

Published January 2, 2020 Irish Times Closed
Tags: 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].

DNA-colour

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Having your Christmas Cake and Eating it

Published December 19, 2019 Irish Times Closed
Tags: 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].

Image from https://www.irishcentral.com/%5D

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A New Mathematical Discovery from Neutrino Physics

Published December 5, 2019 Irish Times Closed
Tags: 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].

Neutrino trails in a bubble chamber [image from Physics World]

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Airport Baggage Screening with X-Ray Tomography

Published November 21, 2019 Irish Times Closed
Tags: 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].

3D X-ray image of baggage [image from Rapiscan Systems ].

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The Vastness of Mathematics: No One Knows it All

Published November 7, 2019 Irish Times Closed
Tags: 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].

The Princeton Companions to Maths and Applied Maths

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Maths and Poetry: Beauty is the Link

Published October 17, 2019 Irish Times Closed
Tags: 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].

Irish postage stamp issued in 2005, on the 200^th anniversary of the birth of William Rowan Hamilton.

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Emergence of Complex Behaviour from Simple Roots

Published October 3, 2019 Irish Times Closed
Tags: 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.

A murmuration of starlings at dusk near Ballywilliam, Co Wexford. Photograph: Cyril Byrne.

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George Salmon, Mathematician & Theologian

Published September 19, 2019 Irish Times Closed
Tags: History

George Salmon (1819-1904) [Image: MacTutor]

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].

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An English Lady with a Certain Taste

Published September 5, 2019 Irish Times Closed
Tags: Statistics

Ronald Fisher in 1913

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].

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Stokes’s 200th Birthday Anniversary

Published August 8, 2019 Irish Times Closed
Tags: 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.

Navier-Stokes-Equations

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Algorithms: Recipes for Success

Published August 1, 2019 Irish Times Closed
Tags: 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].

Continue reading ‘Algorithms: Recipes for Success’

Learning Maths without even Trying

Published July 18, 2019 Irish Times Closed
Tags: 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].

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What did the Romans ever do for Maths?

Published July 4, 2019 Irish Times Closed
Tags: 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].

Roman aqueduct at Segovia, Spain.

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Simple Curves that Perplex Mathematicians and Inspire Artists

Published June 20, 2019 Irish Times Closed
Tags: 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].

Detail from Michaelangelo’s The Creation of Adam, and a Jordan Curve representation [image courtesy of Prof Robert Bosch, Oberlin College. Downloaded from here].

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Spin-off Effects of the Turning Earth

Published June 6, 2019 Irish Times Closed
Tags: Fluid Dynamics, Geophysics, Numerical Weather Prediction

Gaspard-Gustave de Coriolis (1792-1843).

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.

Continue reading ‘Spin-off Effects of the Turning Earth’

Kepler’s Vanishing Circles Hidden in Hamilton’s Hodograph

Published May 2, 2019 Irish Times Closed
Tags: 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].

Left: Elliptic orbit with velocity vectors. Right: Hodograph, with all velocity vectors plotted from a single point.

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

Closing the Gap between Prime Numbers

Published April 18, 2019 Irish Times Closed
Tags: 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].

Yitang Zhang

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A Pioneer of Climate Modelling and Prediction

Published April 4, 2019 Irish Times Closed
Tags: Climate Modelling, Numerical Weather Prediction

Norman Phillips (1923-2019)

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 Closed
Tags: 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].

Greenhouse Effect [Image Wikimedia Commons]

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Hokusai’s Great Wave and Roguish Behaviour

Published March 7, 2019 Irish Times Closed
Tags: Wave Motion

Hokusai’s woodcut “The Great Wave off Kanagawa”.

“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 Closed
Tags: 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].

Axel Thue (1863-1922) and Marston Morse (1892-1977)

Continue reading ‘Multiple Discoveries of the Thue-Morse Sequence’

Rambling and Reckoning

Published February 7, 2019 Irish Times Closed
Tags: 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].

Daily average flow (cubic metres per second) at Ardnacrusha, on the Shannon near Limerick. Data from the Electricity Supply Board (ESB).

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 Closed
Tags: 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].

Pierre de Fermat and Srinivasa Ramanujan, two brilliant “amateur” mathematicians.

Continue reading ‘Discoveries by Amateurs and Distractions by Cranks’

Trappist-1 & the Age of Aquarius

Published January 3, 2019 Irish Times Closed
Tags: 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].

Artist’s impressions of the TRAPPIST-1 planetary system

Artist’s impression of the Trappist-1 planetary system. Image from https://www.eso.org/public/images/eso1805b/

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’

Consider a Spherical Christmas Tree

Published December 20, 2018 Irish Times Closed
Tags: Algorithms, Topology

ChristmasTreeLights

A minor seasonal challenge is how to distribute the fairy lights evenly around the tree, with no large gaps or local clusters. Since the lights are strung on a wire, we are not free to place them individually but must weave them around the branches, attempting to achieve a pleasing arrangement. Optimization problems like this occur throughout applied mathematics [TM153 or search for “thatsmaths” at irishtimes.com].

Trees are approximately conical in shape and we may assume that the lights are confined to the surface of a cone. The peak, where the Christmas star is placed, is a mathematical singularity: all the straight lines that can be drawn on the cone, the so-called generators, pass through this point. Cones are developable surfaces: they can be flattened out into a plane without being stretched or shrunk.

Continue reading ‘Consider a Spherical Christmas Tree’

Random Numbers Plucked from the Atmosphere

Published December 6, 2018 Irish Times Closed
Tags: Number Theory

Randomness is a slippery concept, defying precise definition. A simple example of a random series is provided by repeatedly tossing a coin. Assigning “1” for heads and “0” for tails, we generate a random sequence of binary digits or bits. Ten tosses might produce a sequence such as 1001110100. Continuing thus, we can generate a sequence of any length having no discernible pattern [TM152 or search for “thatsmaths” at irishtimes.com].

Lightning-01

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The “Napoleon of Crime” and The Laws of Thought

Published November 15, 2018 Irish Times Closed
Tags: History, Logic

NewLightOnGBoole A fascinating parallel between a brilliant mathematician and an arch-villain of crime fiction is drawn in a forthcoming book – New Light on George Boole – by Des MacHale and Yvonne Cohen. Professor James Moriarty, master criminal and nemesis of Sherlock Holmes, was described by the detective as “the Napoleon of crime”. The book presents convincing evidence that Moriarty was inspired by Professor George Boole [TM151, or search for “thatsmaths” at irishtimes.com].

Continue reading ‘The “Napoleon of Crime” and The Laws of Thought’

Johannes Kepler and the Song of the Earth

Published November 1, 2018 Irish Times Closed
Tags: Astronomy, Music

Johannes Kepler, German mathematician and astronomer, sought to explain the solar system in terms of divine harmony. His goal was to find a system of the world that was mathematically correct and harmonically pleasing. His methodology was scientific in that his hypotheses were inspired by and confirmed by observations. However, his theological training and astrological interests influenced his thinking [TM150, or search for “thatsmaths” at irishtimes.com].

The six planets known to Kepler [Image NASA].

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Who Uses Maths? Almost Everyone!

Published October 18, 2018 Irish Times Closed
Tags: Education

In the midst of Maths Week Ireland, many students may be asking “What use is mathematics and what purpose is served by studying it?” Mathematicians often stress the inherent beauty and intellectual charm of the subject, but that is unlikely to persuade many people, who demand to know how mathematics can be of use and value to them. [TM149, or search for “thatsmaths” at irishtimes.com].

In reality, mathematics is essential in numerous contexts: the diversity is remarkable, and you may be surprised how maths plays a vital role in the everyday work of so many people.

Continue reading ‘Who Uses Maths? Almost Everyone!’

The Many Modern Uses of Quaternions

Published October 4, 2018 Irish Times Closed
Tags: Algebra, Hamilton

Hamiltons-Bridge-Plaque The story of William Rowan Hamilton’s discovery of new four-dimensional numbers called quaternions is familiar. The solution of a problem that had bothered him for years occurred to him in a flash of insight as he walked along the Royal Canal in Dublin. But this Eureka moment did not arise spontaneously: it was the result of years of intense effort. The great French mathematician Henri Poincaré also described how sudden inspiration occurs unexpectedly, but always following a period of concentrated research [TM148, or search for “thatsmaths” at irishtimes.com].

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Tom Lehrer: Comical Musical Mathematical Genius

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

TomLehrer-SongBook

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].

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The Miraculous Spiral on Booterstown Strand

Published August 16, 2018 Irish Times Closed
Tags: biology, Geometry, Geophysics

We all know what a spiral looks like. Or do we? Ask your friends to describe one and they will probably trace out the form of a winding staircase. But that is actually a helix, a curve in three-dimensional space. A spiral is confined to a plane – it is a flat curve. In general terms, a spiral is formed by a point moving around a fixed centre while its distance increases or decreases as it revolves [see TM145, or search for “thatsmaths” at irishtimes.com].

The spiral sandbank on Booterstown strand (satellite image digitally enhanced by Andrew Lynch).

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Tides: a Tug-of-War between Earth, Moon and Sun

Published August 2, 2018 Irish Times Closed
Tags: Fluid Dynamics, Geophysics

All who set a sail, cast a hook or take a dip have a keen interest in the water level, and the regular ebb and flow of the tides. At most places the tidal variations are semi-diurnal, with high and low water twice each day [see TM144, or search for “thatsmaths” at irishtimes.com].

Animation of tide prediction machine, showing outputs for New York (semi-diurnal tides) and Kuril Islands (diurnal tides) [Source: American Mathematical Society (see below)].

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The Empty Set is Nothing to Worry About

Published July 19, 2018 Irish Times Closed
Tags: Arithmetic, Set Theory

Today’s article is about nothing: nothing at all, as encapsulated in the number zero and the empty set. It took humanity millennia to move beyond the counting numbers. Zero emerged in several civilizations, first as a place-holder to denote a space or gap between digits, and later as a true number, which could be manipulated like any other. [see TM143, or search for “thatsmaths” at irishtimes.com].

A selection of images of zero (google images).

Continue reading ‘The Empty Set is Nothing to Worry About’

Trigonometric Comfort Blankets on Hilltops

Published July 5, 2018 Irish Times Closed
Tags: Geophysics, Maps, Spherical Trigonometry

On a glorious sunny June day we reached the summit of Céidín, south of the Glen of Imall, to find a triangulation station or trig pillar. These concrete pillars are found on many prominent peaks throughout Ireland, and were erected to aid in surveying the country [see TM142, or search for “thatsmaths” at irishtimes.com].

Trig pillar on summit of Croaghan Moira, Wicklow [Image from https://mountainviews.ie/%5D.

Continue reading ‘Trigonometric Comfort Blankets on Hilltops’

Optical Refinements at the Parthenon

Published June 21, 2018 Irish Times Closed
Tags: Geometry, History

The Parthenon is a masterpiece of symmetry and proportion. This temple to the Goddess Athena was built with pure white marble quarried at Pentelikon, about 20km from Athens. It was erected without mortar or cement, the stones being carved to great accuracy and locked together by iron clamps. The building and sculptures were completed in just 15 years, between 447 and 432 BC. [TM141 or search for “thatsmaths” at irishtimes.com].

Parthenon-Photo

Continue reading ‘Optical Refinements at the Parthenon’

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