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].
Archive for the 'Irish Times' Category
The Many Modern Uses of Quaternions
Published October 4, 2018 Irish Times 1 CommentTags: Algebra, Hamilton
Tom Lehrer: Comical Musical Mathematical Genius
Published September 20, 2018 Irish Times Leave a CommentTags: Education, Music, Recreational Maths
Tom Lehrer, mathematician, singer, songwriter and satirist, was born in New York ninety years ago. He was active in public performance for about 25 years from 1945 to 1970. He is most renowned for his hilarious satirical songs, many of which he recorded and which are available today on YouTube [see TM147, or search for “thatsmaths” at irishtimes.com].
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Face Recognition
Published September 6, 2018 Irish Times Leave a CommentTags: Algorithms, Computer Science, Social attitudes
As you pass through an airport, you are photographed several times by security systems. Face recognition systems can identify you by comparing your digital image to faces stored in a database. This form of identification is gaining popularity, allowing you to access online banking without a PIN or password. [see TM146, or search for “thatsmaths” at irishtimes.com].
Jimmy Wales, co-founder of Wikipedia, answering a question. Face detection indicated by squares.
The Miraculous Spiral on Booterstown Strand
Published August 16, 2018 Irish Times Leave a CommentTags: 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 CommentTags: 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 CommentTags: 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).
Trigonometric Comfort Blankets on Hilltops
Published July 5, 2018 Irish Times Leave a CommentTags: 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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