The Popcorn Function

Continuity is not what it seems. In 1875, the German mathematician Carl Johannes Thomae defined a function P(x) with the following extraordinary property: P(x) is discontinuous if x is rational P(x) is continuous if x is irrational. A graph of this function on the interval (0,1) is shown below. The function has many names. We … Continue reading The Popcorn Function →

Carving up the Globe

This week, That’s Maths (TM007) describes various ways of dividing up the sphere. This is an important problem in geometry, biology, chemistry, astronomy, meteorology and climate modelling. The problem of defining a uniform distribution of points on the sphere has challenged mathematicians for centuries. The vertices of the five Platonic solids achieve this but, in … Continue reading Carving up the Globe →

Falling Slinky

If you drop a slinky from a hanging position, something very surprising happens. The bottom remains completely motionless until the top, collapsing downward coil upon coil, crashes into it. How can this be so? We all know that anything with mass is subject to gravity, and this is certainly true of the lower coils of … Continue reading Falling Slinky →

Contagion

This week, That’s Maths (TM006) describes the use of mathematical models to study the spread of infections like the SARS epidemic and swine flu. Simple models such as the SIR model of Kermack and McKendrick (1927) can simulate the broad features of epidemics, but much more sophisticated models have been developed using the same approach. … Continue reading Contagion →