Curves with Singularities

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.

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’

How Big was the Bomb?

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.

US army soldiers watching the first test of an atomic weapon, the Trinity Test.

Continue reading ‘How Big was the Bomb?’

Cartoon Curves

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.

Yogi Bear Curve. The Mathematica command to generate this is given below.

Continue reading ‘Cartoon Curves’

The Biggest Harp in Ireland

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”.

Image from TIger Dublin Fringe Festival website: http://fringefest.com/programme/harp-a-river-cantata Photo Credit: Ciara Corrigan

Image from Tiger Dublin Fringe Festival website.
Photo Credit: Ciara Corrigan

Continue reading ‘The Biggest Harp in Ireland’

Temperamental Tuning

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.

Piano-Keyboard-1octave Continue reading ‘Temperamental Tuning’

Biomathematics: the New Frontier

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]

Biological network modelled by Boris Kholodenko, SBI.
[Frosted vinyl print on wall of SBI boardroom in UCD]

Continue reading ‘Biomathematics: the New Frontier’

Do you remember Venn?

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.

RIght: John Venn (1834–1923) with signature. Left: Stained glass window at Gonville & Caius College showing Venn diagram [images Wikimedia Commons].

Left: Stained glass window at Gonville & Caius College, Cambridge showing a Venn diagram. Right: John Venn (1834-1923) with signature [images Wikimedia Commons].

Continue reading ‘Do you remember Venn?’


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