Published December 26, 2013
Tags: Arithmetic, Euler, Number Theory
Many mathematicians spend their time proving results. The (very old) joke is that they are machines for turning coffee into theorems. A theorem is a statement that has been shown, by a sequence of irrefutable steps, to follow logically from a set of fundamental assumptions known as axioms.
These axioms themselves may be self-evident, or may simply be assumed to be true. Given this, the statement contained in a theorem is known with certainty to be true.
Continue reading ‘Experiment and Proof’
Published December 19, 2013
Tags: Fractals, Maps
The article in this week’s That’s Maths column in the Irish Times ( TM035 ) is about the remarkable Christmas Eve journey of Santa Claus.
Continue reading ‘Santa’s Fractal Journey’
Published December 12, 2013
Tags: Fractals, Ireland, Maps
Reports of the length of Ireland’s coastline vary widely. The World Factbook of the Central Intelligence Agency gives a length of 1448 km. The Ordnance Survey of Ireland has a value of 3,171 km (http://www.osi.ie). The World Resources Institute, using data from the United States Defense Mapping Agency, gives 6,347km (see Wikipedia article ).
Continue reading ‘Ireland’s Fractal Coastline’