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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. Continue reading ‘The Popcorn Function’
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. Continue reading ‘Carving up the Globe’
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? Continue reading ‘Falling Slinky’
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.
For an elementary introduction to the mthematics of modelling infectious diseases, see Epidemic Modelling, by D. J. Daley and J. Gani, Cambridge Univ. Press, 1999.
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