Published September 25, 2014
Tags: Analysis, Geometry
Many of the curves that we study are smooth, with a well-defined tangent at every point. Points where the derivative is defined — where there is a definite slope — are called regular points. However, many curves also have exceptional points, called singularities. If the derivative is not defined at a point, or if it does not have a unique value there, the point is singular.
Slinky traces a smooth helical curve in three dimensions.
Generally, if we zoom in close to a point on a curve, the curve looks increasingly like a straight line. However, at a singularity, it may look like two lines crossing or like two lines whose slopes converge as the resolution increases. Continue reading ‘Curves with Singularities’
By a brilliant application of dimensional analysis, G.I.Taylor estimated the explosive energy of the first atomic blast, the Trinity Test (see this week’s That’s Maths column in The Irish Times, TM053, or search for “thatsmaths” at irishtimes.com).
US army soldiers watching the first test of an atomic weapon, the Trinity Test.
Continue reading ‘How Big was the Bomb?’
The powerful and versatile computational software program called Mathematica is widely used in science, engineering and mathematics. There is a related system called Wolfram Alpha, a computational knowledge engine, that can do Mathematica calculations and that runs on an iPad.
Yogi Bear Curve. The Mathematica command to generate this is given below.
Continue reading ‘Cartoon Curves’
This week’s That’s Maths column in The Irish Times (TM052, or search for “thatsmaths” at irishtimes.com) is about “Samuel Beckett Playing Bridge in Dublin”.
Continue reading ‘The Biggest Harp in Ireland’
Published August 28, 2014
Tags: Music, Pythagoras
Every pure musical tone has a frequency, the number of oscillations per second in the sound wave. Doubling the frequency corresponds to moving up one octave. A musical note consists of a base frequency or pitch, called the fundamental together with a series of harmonics, or oscillations whose frequencies are whole-number multiples of the fundamental frequency.
Continue reading ‘Temperamental Tuning’
Published August 21, 2014
Mathematics is coming to Life in a Big Way. This week’s That’s Maths in The Irish Times (TM051, or Search for “thatsmaths” at irishtimes.com) is about the increasing importance of mathematics in the biological sciences.
Biological network modelled by Boris Kholodenko, SBI.
[Frosted vinyl print on wall of SBI boardroom in UCD]
Continue reading ‘Biomathematics: the New Frontier’
Published August 14, 2014
Tags: History, Set Theory
Do you recall coming across those diagrams with overlapping circles that were popularised in the ‘sixties’, in conjunction with the “New Maths”. They were originally introduced around 1880 by John Venn, and now bear his name.
Continue reading ‘Do you remember Venn?’
Left: Stained glass window at Gonville & Caius College, Cambridge showing a Venn diagram. Right: John Venn (1834-1923) with signature [images Wikimedia Commons].