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The Miraculous Spiral on Booterstown Strand

Published August 16, 2018 Irish Times Leave a Comment
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 Leave a Comment
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 Leave a Comment
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).

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Trigonometric Comfort Blankets on Hilltops

Published July 5, 2018 Irish Times Leave a Comment
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.

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Optical Refinements at the Parthenon

Published June 21, 2018 Irish Times Leave a Comment
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

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Leopold Bloom’s Arithmetical Adventures

Published June 7, 2018 Irish Times Leave a Comment
Tags: Arithmetic, Puzzles

As Bloomsday approaches, we reflect on James Joyce and mathematics. Joyce entered UCD in September 1898. His examination marks are recorded in the archives of the National University of Ireland, and summarized in a table in Richard Ellmann’s biography of Joyce (reproduced below) [TM140 or search for “thatsmaths” at irishtimes.com].

Joyce’s examination marks [archives of the National University of Ireland].

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Mathematics at the Science Museum

Published May 17, 2018 Irish Times Leave a Comment
Tags: Education, History

The new Winton Gallery at London’s Science Museum in South Kensington holds a permanent display on the history of mathematics over the past 400 years. The exhibition shows how mathematics has underpinned astronomy, navigation and surveying in the past, and how it continues to pervade the modern world [see TM139, or search for “thatsmaths” at irishtimes.com].

Central Display at the Science Museum

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Stan Ulam, a mathematician who figured how to initiate fusion

Published May 3, 2018 Irish Times Leave a Comment
Tags: Algorithms, Fluid Dynamics, Set Theory, Topology

Stanislaw Ulam, born in Poland in 1909, was a key member of the remarkable Lvov School of Mathematics, which flourished in that city between the two world wars. Ulam studied mathematics at the Lvov Polytechnic Institute, getting his PhD in 1933. His original research was in abstract mathematics, but he later became interested in a wide range of applications. He once joked that he was “a pure mathematician who had sunk so low that his latest paper actually contained numbers with decimal points” [TM138 or search for “thatsmaths” at irishtimes.com].

Operation Castle, Bikini Atoll, 1954

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Geodesics on the Spheroidal Earth-II

Published April 19, 2018 Irish Times Leave a Comment
Tags: Geometry, Geophysics, Navigation, Pythagoras

Geodesy is the study of the shape and size of the Earth, and of variations in its gravitational field. The Earth was originally believed to be flat, but many clues, such as the manner in which ships appear and disappear at the horizon, and the changed perspective from an elevated vantage point, as well as astronomical phenomena, convinced savants of its spherical shape. In the third century BC, Eratosthenes accurately estimated the circumference of the Earth [TM137 or search for “thatsmaths” at irishtimes.com].

Geodesic at bearing of 60 degrees from Singapore. Passes close to Quito, Ecuador. Note that it is not a closed curve: it does not return to Singapore.

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Fourier’s Wonderful Idea – II

Published April 5, 2018 Irish Times Leave a Comment
Tags: Analysis, History

Solving PDEs by a Roundabout Route

Joseph Fourier (1768-1830)

Joseph Fourier, born just 250 years ago, introduced a wonderful idea that revolutionized science and mathematics: any function or signal can be broken down into simple periodic sine-waves. Radio waves, micro-waves, infra-red radiation, visible light, ultraviolet light, X-rays and gamma rays are all forms of electromagnetic radiation, differing only in frequency [TM136 or search for “thatsmaths” at irishtimes.com].

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Cubic Skulduggery & Intrigue

Published March 15, 2018 Irish Times Leave a Comment
Tags: Algebra, History

Solution of a cubic equation, usually called Cardano’s formula.

Babylonian mathematicians knew how to solve simple polynomial equations, in which the unknown quantity that we like to call x enters in the form of powers, that is, x multiplied repeatedly by itself. When only x appears, we have a linear equation. If x-squared enters, we have a quadratic. The third power of x yields a cubic equation, the fourth power a quartic and so on [TM135 or search for “thatsmaths” at irishtimes.com].

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Reducing R-naught to stem the spread of Epidemics

Published March 1, 2018 Irish Times Leave a Comment
Tags: Epidemiology, medicine

Vaccine-1 We are reminded each year to get vaccinated against the influenza virus. The severity of the annual outbreak is not known with certainty in advance, but a major pandemic is bound to occur sooner or later. Mathematical models play an indispensable role in understanding and managing infectious diseases. Models vary in sophistication from the simple SIR model with just three variables to highly complex simulation models with millions of variables [TM134 or search for “thatsmaths” at irishtimes.com]. Continue reading ‘Reducing R-naught to stem the spread of Epidemics’

Galileo’s Book of Nature

Published February 15, 2018 Irish Times Leave a Comment
Tags: Astronomy, History, Mechanics

In 1971, astronaut David Scott, standing on the Moon, dropped a hammer and a feather and found that both reached the surface at the same time. This popular experiment during the Apollo 15 mission was a dramatic demonstration of a prediction made by Galileo three centuries earlier. Galileo was born in Pisa on 15 February 1564, just 454 years ago today [TM133 or search for “thatsmaths” at irishtimes.com].

Image: NASA

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Staying Put or Going with the Flow

Published February 1, 2018 Irish Times Leave a Comment
Tags: Algorithms, Geophysics, Numerical Analysis

The atmospheric temperature at a fixed spot may change in two ways. First, heat sources or sinks may increase or decrease the thermal energy; for example, sunshine may warm the air or radiation at night may cool it. Second, warmer or cooler air may be transported to the spot by the air flow in a process called advection. Normally, the two mechanisms act together, sometimes negating and sometimes reinforcing each other. What is true for temperature is also true for other quantities: pressure, density, humidity and even the flow velocity itself. This last effect may be described by saying that “the wind blows the wind” [TM132 or search for “thatsmaths” at irishtimes.com].

Hurricane Ophelia approaching Ireland, 16 October 2017, 1200Z. Image from https://earth.nullschool.net/

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The Heart of Mathematics

Published January 18, 2018 Irish Times Leave a Comment
Tags: biology, Fluid Dynamics, medicine

At five litres per minute the average human heart pumps nearly 200 megalitres of blood through the body in a lifetime. Heart disease causes 40 percent of deaths in the EU and costs hundreds of billions of Euros every year. Mathematics can help to improve our knowledge of heart disease and our understanding of cardiac malfunction [TM131 or search for “thatsmaths” at irishtimes.com].

Cardiogram

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Energy Cascades in Van Gogh’s Starry Night

Published January 4, 2018 Irish Times Leave a Comment
Tags: Fluid Dynamics, Geophysics

“Big whirls have little whirls that feed on their velocity,
And little whirls have lesser whirls, and so on to viscosity.“

We are all familiar with the measurement of speed, the distance travelled in a given time. Allowing for the direction as well as the magnitude of movement, we get velocity, a vector quantity. In the flow of a viscous fluid, such as treacle pouring off a spoon, the velocity is smooth and steady. Such flow is called laminar, and variations of velocity from place to place are small. By contrast, the motion of the atmosphere, a fluid with low viscosity, can be irregular and rapidly fluctuating. We experience this when out and about on a gusty day. Such chaotic fluid flow is called turbulence, and this topic continues to challenge the most brilliant scientists [TM130 or search for “thatsmaths” at irishtimes.com].

Vincent Van Gogh’s Starry Night.

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Darker Mornings, Brighter Evenings

Published December 21, 2017 Irish Times Leave a Comment
Tags: Astronomy, Time measurement

Today is the winter solstice, the shortest day of the year. We might expect that the latest sunrise and earliest sunset also occur today. In fact, the earliest sunset, the darkest day of the year, was on 13 December, over a week ago, and the latest sunrise is still more than a week away. This curious behaviour is due to the unsteady path of the Earth around the Sun. Our clocks, which run regularly at what is called mean time, move in and out of synchronization with solar time [TM129 or search for “thatsmaths” at irishtimes.com].

Sunrise in Newgrange on winter solstice [image from http://www.boynevalleytours.com/

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The Star of Bethlehem … or was it a Planet?

Published December 7, 2017 Irish Times 1 Comment
Tags: Astronomy

People of old were more aware than we are of the night sky and took a keen interest in unusual happenings above them. The configuration of the stars was believed to be linked to human affairs and many astronomical phenomena were interpreted as signs of good or evil in the offing. The Three Wise Men or Magi were astrologers, experts in celestial matters, and would have drawn inferences from what they observed in the sky [TM128 or search for “thatsmaths” at irishtimes.com].

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Slingshot Orbit to Asteroid Bennu

Published November 16, 2017 Irish Times Leave a Comment
Tags: Astronomy, Mechanics

The Voyager 1 and Voyager 2 spacecraft have now left the solar system and will continue into deep space. How did we manage to send them so far? The Voyager spacecraft used gravity assists to visit Jupiter, Saturn, Uranus and Neptune in the late 1970s and 1980s. Gravity assist manoeuvres, known as slingshots, are essential for interplanetary missions. They were first used in the Soviet Luna-3 mission in 1959, when images of the far side of the Moon were obtained. Space mission planners use them because they require no fuel and the gain in speed dramatically shortens the time of missions to the outer planets.

Artist’s impression of OSIRIS-REx orbiting Bennu [Photo Credit: NASA]

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Modular Arithmetic: from Clock Time to High Tech

Published November 2, 2017 Irish Times Leave a Comment
Tags: Arithmetic, Time measurement

You may never have heard of modular arithmetic, but you use it every day without the slightest difficulty. In this system, numbers wrap around when they reach a certain size called the modulus; it is the arithmetic of remainders [TM126 or search for “thatsmaths” at irishtimes.com].

We use modular arithmetic for timekeeping with a 12-hour clock [Image Wikimedia Commons]

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Learning Maths has never been Easier

Published October 19, 2017 Irish Times Leave a Comment
Tags: 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].

Eoin Gill and Sheila Donegan with Jadine Rock of Rutland National School, Dublin , at the launch of Maths Week Ireland. Image: Shane O’Neill, SON Photographic.

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From Sailing on a Rhumb to Flying on a Geodesic

Published October 5, 2017 Irish Times Leave a Comment
Tags: Maps, Navigation

If you fly 14,500 km due westward from New York you will come to Beijing. The two cities are on the fortieth parallel of latitude. However, by flying a great circle route over the Arctic, you can reach Beijing in 11,000 km, saving 3,500 km and much time and aviation fuel. [TM124 or search for “thatsmaths” at irishtimes.com].

Great circle route from New York to Beijing (gnomonic projection).

On a gnomonic projection (as above) each point on the Earth’s surface is projected from the centre of the Earth onto a plane tangent to the globe. On this map, great circles appear as straight lines.

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Andrey Markov’s Brilliant Ideas are still a Driving Force

Published September 21, 2017 Irish Times Leave a Comment
Tags: Algorithms, Statistics

A A Markov (1856-1922)

Imagine examining the first 20,000 letters of a book, counting frequencies and studying patterns. This is precisely what Andrey Markov did when he analyzed the text of Alexander Pushkin’s verse novel Eugene Onegin. This work comprises almost 400 stanzas of iambic tetrameter and is a classic of Russian literature. Markov studied the way vowels and consonants alternate and deduced the probabilities of a vowel being followed by a another vowel, by a consonant, and so on. He was applying a statistical model that he had developed in 1906 and that we now call a Markov Process or Markov chain. [TM123 or search for “thatsmaths” at irishtimes.com].

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Euler and the Fountains of Sanssouci

Published September 7, 2017 Irish Times Leave a Comment
Tags: Applied Maths, Euler, Fluid Dynamics

When Frederick the Great was crowned King of Prussia in 1740 he immediately revived the Berlin Academy of Sciences and invited scholars from throughout Europe to Berlin. The most luminous of these was Leonhard Euler, who arrived at the academy in 1741. Euler was an outstanding genius, brilliant in both mathematics and physics. Yet, a myth persists that he failed spectacularly to solve a problem posed by Frederick. Euler is reputed to have bungled his mathematical analysis. In truth, there was much bungling, but the responsibility lay elsewhere. [TM122 or search for “thatsmaths” at irishtimes.com].

Sanssouci Palace, the summer home of Frederick the Great in Potsdam.
PHOTO: https://www.flickr.com/photos/b_hurwitz/4064337397/

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It’s as Easy as Pi

Published August 3, 2017 Irish Times Leave a Comment
Tags: Archimedes, Geometry, Number Theory, Pi

Pi-Symbol Every circle has the property that the distance around it is just over three times the distance across. This has been known since the earliest times [see TM120 or search for “thatsmaths” at irishtimes.com].

The constant ratio of the circumference to the diameter, denoted by the Greek letter pi, is familiar to every school-child. You might expect to find a proof in Euclid’s Elements of Geometry, he could not prove it, and he made no mention of the ratio (see last week’s post).

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Quadrivium: The Noble Fourfold Way

Published July 20, 2017 Irish Times Leave a Comment
Tags: Arithmetic, Astronomy, Geometry, History, Music

According to Plato, a core of mathematical knowledge – later known as the Quadrivium – was essential for an understanding of the Universe. The curriculum was outlined in Plato’s Republic. The name Quadrivium means four ways, but this term was not used until the time of Boethius in the 6^th century AD [see TM119 or search for “thatsmaths” at irishtimes.com].

Image from here.

It is said that an inscription over the entrance to Plato’s Academy read “Let None But Geometers Enter Here”. This indicated that the Quadrivium was a prerequisite for the study of philosophy in ancient Greece.

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Robert Murphy, a “Brilliant Meteor”

Published July 6, 2017 Irish Times Leave a Comment
Tags: History, Ireland

“A brilliant meteor that flared intensely but all too briefly”; this was how Des MacHale described the Cork-born mathematician Robert Murphy in his biography of George Boole, first professor of mathematics in Cork. Murphy was a strong influence on Boole, who quoted liberally from his publications [see TM118 or search for “thatsmaths” at irishtimes.com].

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Fractal Complexity of Finnegans Wake

Published June 15, 2017 Irish Times Leave a Comment
Tags: Algorithms, Fractals

Tomorrow we celebrate Bloomsday, the day of action in Ulysses. Most of us regard Joyce’s singular book as a masterpiece, even if we have not read it. In contrast, Finnegans Wake is considered by some as a work of exceptional genius, by others as impenetrable bafflegab [See TM117 or search for “thatsmaths” at irishtimes.com].

Wavelet transform of sentence length sequence in Ulysses. Note the structural change around sentence number 13,000. Image from Drozdz, et al (2016).

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Beautiful Patterns in Maths and Music

Published June 1, 2017 Irish Times Leave a Comment
Tags: Music

The numerous connections between mathematics and music have long intrigued practitioners of both. For centuries scholars and musicians have used maths to analyze music and also to create it. Many of the great composers had a deep understanding of the mathematical principles underlying music. Johann Sebastian Bach was the grand master of structural innovation and invention in music. While his compositions are the free creations of a genius, they have a fundamentally mathematical basis [See TM116 or search for “thatsmaths” at irishtimes.com].

Johann Sebastian Bach, the grand master of structural innovation and invention in music.

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Yves Meyer wins 2017 Abel Prize

Published May 18, 2017 Irish Times Leave a Comment
Tags: Applied Maths, Wave Motion

On 23 May King Harald V of Norway will present the Abel Prize to French mathematician Yves Meyer. Each year, the prize is awarded to a laureate for “outstanding work in the field of mathematics”. Comparable to a Nobel Prize, the award is named after the exceptional Norwegian, Niels Henrik Abel who, in a short life from 1802 to 1829, made dramatic advances in mathematics. Meyer was chosen for his development of the mathematical theory of wavelets. [See TM115 or search for “thatsmaths” at irishtimes.com].

Yves-Meyer-Wide

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When Roughly Right is Good Enough

Published May 4, 2017 Irish Times Leave a Comment
Tags: Algorithms, Education

How high is Liberty Hall? How fast does human hair grow? How many A4 sheets of paper would cover Ireland? How many people in the world are talking on their mobile phones right now? These questions seem impossible to answer but, using basic knowledge and simple logic, we can make a good guess at the answers. For example, Liberty Hall has about 16 floors. With 4 metres per floor we get a height of 64 metres, close enough to the actual height. Problems of this nature are known as Fermi problems. [TM114 or search for “thatsmaths” at irishtimes.com].

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The Water is Rising Fast

Published April 20, 2017 Irish Times Leave a Comment
Tags: Fluid Dynamics, Geophysics

Seventy percent of the Earth is covered by water and three quarters of the world’s great cities are on the coast. Ever-rising sea levels pose a real threat to more than a billion people living beside the sea. As the climate warms, this is becoming a greater threat every year [TM113 or search for “thatsmaths” at irishtimes.com].

Mean Sea level in Seattle from 1900 to 2013

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The Improbability Principle

Published April 6, 2017 Irish Times Leave a Comment
Tags: Probability, Statistics

Extremely improbable events are commonplace.

“It’s an unusual day if nothing unusual happens”. This aphorism encapsulates a characteristic pattern of events called the Improbability Principle. Popularised by statistician Sir David Hand, emeritus professor at Imperial College London, it codifies the paradoxical idea that extremely improbable events happen frequently. [TM112 or search for “thatsmaths” at irishtimes.com].

From front cover of The Improbability Principle

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A Life-saving Whirligig

Published March 16, 2017 Irish Times 2 Comments
Tags: Mechanics, medicine

Modern science is big: the gravitational wave detector (LIGO) cost over a billion dollars, and the large hadron collider (LHC) in Geneva took decades to build and cost almost five billion euros. It may seem that scientific advances require enormous financial investment. So, it is refreshing to read in Nature Biomedical Engineering (Vol 1, Article 9) about the development of an ultra-cheap centrifuge that costs only a few cents to manufacture [TM111 or search for “thatsmaths” at irishtimes.com].

Whirligig, made from a plastic disk and handles and some string

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Enigmas of Infinity

Published March 2, 2017 Irish Times Leave a Comment
Tags: Analysis, History, Logic

Children sometimes amuse themselves searching for the biggest number. After trying millions, billions and trillions, they realize that there is no end to the game: however big a number may be, we can always add 1 to produce a bigger number: the set of counting numbers is infinite. The concept of infinity has intrigued philosophers since antiquity, and it leads to many surprises and paradoxical results [TM110 or search for “thatsmaths” at irishtimes.com].

infinity-symbols

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The Spire of Light

Published February 16, 2017 Irish Times Leave a Comment
Tags: Applied Maths, Mechanics

Towering over O’Connell Street in Dublin, the Spire of Light, at 120 metres, is about three times the height of its predecessor [TM109 or search for “thatsmaths” at irishtimes.com]. The Spire was erected in 2003, filling the void left by the destruction in 1966 of Nelson’s Pillar. The needle-like structure is a slender cone of stainless steel, the diameter tapering from 3 metres at the base to 15 cm at its apex. The illumination from the top section shines like a beacon throughout the city.

spire-nightscape

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Voronoi Diagrams: Simple but Powerful

Published February 2, 2017 Irish Times 2 Comments
Tags: Algorithms, Geometry

We frequently need to find the nearest hospital, surgery or supermarket. A map divided into cells, each cell covering the region closest to a particular centre, can assist us in our quest. Such a map is called a Voronoi diagram, named for Georgy Voronoi, a mathematician born in Ukraine in 1868. He is remembered today mostly for his diagram, also known as a Voronoi tessellation, decomposition, or partition. [TM108 or search for “thatsmaths” at irishtimes.com].

Voronoi diagram drawn using the applet of Paul Chew (see Sources below).

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The Library of Babel and the Information Explosion

Published January 19, 2017 Irish Times Leave a Comment
Tags: Arithmetic, Topology

The world has been transformed by the Internet. Google, founded just 20 years ago, is a major force in online information. The company name is a misspelt version of “googol”, the number one followed by one hundred zeros. This name echoes the vast quantities of information available through the search engines of the company [TM107 or search for “thatsmaths” at irishtimes.com].

Artist’s impression of the Library of Babel [Image from Here].

Long before the Internet, the renowned Argentine writer, poet, translator and literary critic Jorge Luis Borges (1889 – 1986) envisaged the Universe as a vast information bank in the form of a library. The Library of Babel was imagined to contain every book that ever was or ever could be written.

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The Edward Worth Library: a Treasure Trove of Maths

Published December 15, 2016 Irish Times 1 Comment
Tags: History

Infinite Riches in a Little Room. Christopher Marlowe.

The Edward Worth Library may be unknown to many readers. Housed in Dr Steevens’ Hospital, Dublin, now an administrative centre for the Health Service Executive, the library was collected by hospital Trustee Edward Worth, and bequeathed to the hospital after his death in 1733. The original book shelves and cases remain as they were in the 1730s. The collection is catalogued online. [TM105 or search for “thatsmaths” at irishtimes.com].

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The Shaky Foundations of Mathematics

Published December 1, 2016 Irish Times Leave a Comment
Tags: Algorithms, Logic, Number Theory

The claim is often made that mathematical results are immutable. Once proven, they remain forever valid. But things are not so simple. There are problems at the very core of mathematics that cast a shadow of uncertainty. We can never be absolutely sure that the foundations of our subject are rock-solid [TM104 or search for “thatsmaths” at irishtimes.com].

Left: Plato and Aristotle. Centre: Pythagoras. Right: Euclid [Raphael, The School of Athens]

The ancient Greeks put geometry on a firm footing. Euclid set down a list of axioms, or basic intuitive assumptions. Upon these, the entire edifice of Euclidean geometry is constructed. This axiomatic approach has been the model for mathematics ever since.

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Marvellous Merchiston’s Logarithms

Published November 17, 2016 Irish Times Leave a Comment
Tags: Applied Maths, History, Numerical Analysis

Log tables, invaluable in science, industry and commerce for 350 years, have been consigned to the scrap heap. But logarithms remain at the core of science, as a wide range of physical phenomena follow logarithmic laws [TM103 or search for “thatsmaths” at irishtimes.com].

Android app RealCalc with natural and common log buttons indicated.

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A New Window on the World

Published November 3, 2016 Irish Times Leave a Comment
Tags: Astronomy, Relativity

The motto of the Pythagoreans was “All is Number” and Pythagoras may have been the first person to imagine that the workings of the world might be understood in mathematical terms. This idea has now brought us to the point where, at a fundamental level, mathematics is the primary means of describing the physical world. Galileo put it this way: the book of nature is written in the language of mathematics [TM102, or search for “thatsmaths” at irishtimes.com].

Visualization of gravitational waves. Image credit MPI/Gravitational Physics/ITP Frankfurt/ZI Berlin.

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Thank Heaven for Turbulence

Published October 20, 2016 Irish Times Leave a Comment
Tags: Applied Maths, Fluid Dynamics

The chaotic flow of water cascading down a mountainside is known as turbulence. It is complex, irregular and unpredictable, but we should count our blessings that it exists. Without turbulence, we would gasp for breath, struggling to absorb oxygen or be asphyxiated by the noxious fumes belching from motorcars, since pollutants would not be dispersed through the atmosphere [TM101, or search for “thatsmaths” at irishtimes.com].

Turbulent flow behind a cylindrical obstacle [image from “An Album of Fluid Motion”, Milton Van Dyke, 1982].

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A Ton of Wonders

Published October 6, 2016 Irish Times Leave a Comment
Tags: Number Theory

Every number is interesting. Suppose there were uninteresting numbers. Then there would be a smallest one. But this is an interesting property, contradicting the supposition. By reductio ad absurdum, there are none!

This is the hundredth “That’s Maths” article to appear in The Irish Times [TM100, or search for “thatsmaths” at irishtimes.com]. To celebrate the event, we have composed an ode to the number 100.

tonofwonders

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The next Hamilton

Published September 15, 2016 Irish Times 1 Comment
Tags: Hamilton, History, Ireland

William Rowan Hamilton was Ireland’s greatest mathematician. His name is heard thousands of times every day throughout the world when researchers use the Hamiltonian function that encapsulates the dynamics of a vast range of physical systems. He achieved fame early in life and remains one of the all-time great scientists. [TM099, or search for “thatsmaths” at irishtimes.com].

hamilton-stamp

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The Tunnel of Eupalinos in Samos

Published September 1, 2016 Irish Times Leave a Comment
Tags: Geometry, Pythagoras

The tunnel of Eupalinos on the Greek island of Samos, over one kilometre in length, is one of the greatest engineering achievements of the ancient world [TM098, or search for “thatsmaths” at irishtimes.com].

Samos-Tunnel-Map

Approximate course of the tunnel of Eupalinos in Samos.

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Recreational Mathematics is Fun

Published August 18, 2016 Irish Times Leave a Comment
Tags: 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].

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

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Can Mathematics Keep Us Secure?

Published August 4, 2016 Irish Times Leave a Comment
Tags: Algorithms, Computer Science

The National Security Agency is the largest employer of mathematicians in America. Mathematics is a core discipline at NSA and mathematicians work on signals intelligence and information security (US citizenship is a requirement for employment). Why is NSA so interested in mathematics? [See TM096, or search for “thatsmaths” at irishtimes.com].

Flag of the National Security Agency

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Computers Speaking in Irish

Published July 21, 2016 Irish Times Leave a Comment
Tags: Computer Science, Education, Ireland

Most of us use computer terminals, tablets and smart phones, absorbing information quickly and easily. How do the many thousands of Irish people who are blind or visually impaired manage to interact with computers? For them, entering data by keyboard or voice is easy, but special software is needed to convert the text on screen into a form for output to a loudspeaker or headphones, or to drive a refreshable Braille display [TM095, or search for “thatsmaths” at irishtimes.com].

Braille display (www.humanware.com)

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