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’