## Archive for August, 2018

### A Zero-Order Front

Sharp gradients known as fronts form in the atmosphere when variations in the wind field bring warm and cold air into close proximity. Much of our interesting weather is associated with the fronts that form in extratropical depressions.

Below, we describe a simple mechanistic model of frontogenesis, the process by which fronts are formed.

### The Flight of the Bumble Bee

Alice and Bob, initially a distance l apart, walk towards each other, each at a speed w. A bumble bee flies from the nose of one to the nose of the other and back again, repeating this zig-zag flight at speed f until Alice and Bob meet. How far does the bumble bee fly?

### The Miraculous Spiral on Booterstown Strand

We all know what a spiral looks like. Or do we? Ask your friends to describe one and they will probably trace out the form of a winding staircase. But that is actually a helix, a curve in three-dimensional space. A spiral is confined to a plane – it is a flat curve. In general terms, a spiral is formed by a point moving around a fixed centre while its distance increases or decreases as it revolves [see TM145, or search for “thatsmaths” at irishtimes.com].

The spiral sandbank on Booterstown strand (satellite image digitally enhanced by Andrew Lynch).

### Euler’s “Degree of Agreeableness” for Musical Chords

The links between music and mathematics stretch back to Pythagoras and many leading mathematicians have studied the theory of music. Music and mathematics were pillars of the Quadrivium, the four-fold way that formed the basis of higher education for thousands of years. Music was a central theme for Johannes Kepler in his Harmonices Mundi – Harmony of the World, and René Descartes’ first work was a compendium of music.

### Tides: a Tug-of-War between Earth, Moon and Sun

All who set a sail, cast a hook or take a dip have a keen interest in the water level, and the regular ebb and flow of the tides. At most places the tidal variations are semi-diurnal, with high and low water twice each day  [see TM144, or search for “thatsmaths” at irishtimes.com].

Animation of tide prediction machine, showing outputs for New York (semi-diurnal tides) and Kuril Islands (diurnal tides) [Source: American Mathematical Society (see below)].