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.

### Biomathematics: the New Frontier

Published August 21, 2014 Irish Times Leave a CommentTags: biology

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.

### Do you remember Venn?

Published August 14, 2014 Occasional Leave a CommentTags: 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?’### “Come See the Spinning Globe”

Published August 7, 2014 Irish Times Leave a CommentTags: Mechanics, Physics

*That’s Maths* in *The Irish Times* this week (TM050, or Search for “thatsmaths” at irishtimes.com) is about how a simple pendulum can demonstrate the rotation of the Earth.

Many of us recall the sense of wonder we felt upon learning that there is no biggest number; for some of us, that wonder has never quite gone away. It is obvious that, given any counting number, one can be added to it to give a larger number. But the implication that there is no limit to this process is perplexing.

### Invention or Discovery?

Published July 24, 2014 Occasional Leave a CommentTags: Analysis, Logic, Number Theory, Social attitudes

Is mathematics invented or discovered? As many great mathematicians have considered this question without fully resolving it, there is little likelihood that I can provide a complete answer here. But let me pose a possible answer in the form of a conjecture:

** Conjecture:*** Definitions are invented. Theorems are discovered.*

The goal is to prove this conjecture, or to refute it. Below, some arguments in support of the conjecture are presented. Continue reading ‘Invention or Discovery?’

### Digital Dentistry

Published July 17, 2014 Irish Times Leave a CommentTags: Computer Science, medicine

*That’s Maths* in *The Irish Times* this week (TM049, or Search for “thatsmaths” at irishtimes.com) is about applications of computer aided design and computer aided manufacture to making dental crowns.