I was interviewed by Nira Chamberlain, President of the Mathematical Association. I am the twelfth person to whom he has asked his question “what is the point of mathematics?” Hoping to offer something a little different, I spoke about teaching students the role mathematical modelling can play in sustainability.
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We all need some space!
A couple of days ago, a question occurred to me:
What’s the furthest I’ve ever been from anyone else?
Upcoming Mathematical Events/Competitions in October 2020
Here’s a round-up of some mathematical events and competitions that might be of interest, happening from October.
Mathematical modelling of Facebook use (video)
Watch mathematician and data scientist Jonny explain mathematical modelling of networks.
Apiological: mathematical speculations about bees (Part 2: Estimating nest volumes)
This is part 2 of a three-part series of mathematical speculations about bees. Part 1 looked at honeycomb geometry.
Honeybees scout for nesting sites in tree cavities and other nooks and crannies, and need to know whether a chamber is large enough to contain all the honey necessary to feed their colony throughout the winter. A volume of less than 10 litres would mean starvation for the whole colony, whereas 45 litres gives a high chance of survival. How are tiny honeybees able to estimate the capacity of these large enclosed spaces, which can be very irregular and have multiple chambers?
Apiological: mathematical speculations about bees (Part 1: Honeycomb geometry)
Bees have encouraged mathematical speculation for two millennia, since classical scholars tried to explain the geometrically appealing shape of honeycombs. How do bees tackle complex problems that humans would express mathematically? In this series we’ll explore three situations where understanding the maths could help explain the uncanny instincts of bees.
Honeycomb geometry
A curvy wild honeycomb.
Honeybees collect nectar from flowers and use it to produce honey, which they then store in honeycombs made of beeswax (in turn derived from honey). A question that has puzzled many inquiring minds across the ages is: why are honeycombs made of hexagonal cells?
The Roman scholar Varro, in his 1st century BC book-long poem De Agri Cultura (“On Agriculture”), briefly states
“Does not the chamber in the comb have six angles, the same number as the bee has feet? The geometricians prove that this hexagon inscribed in a circular figure encloses the greatest amount of space ((Translation by Hooper and Ash in the Loeb. I’ve been told that ‘Hexagonon’ is in its singular form, and the only Greek word (also having Greek grammar) amongst this part of Varro’s Latin text. I would be happier that Varro understood what he was writing about if the text more explicitly described the construction, perhaps ‘Three hexagons encircling a point’, or ‘Six hexagons arranged around a seventh’. In translation, it could be viewed as falsely suggesting that the hexagon is the polygon with the greatest area that fits inside a circle. In his defense though, Varro also earlier suggests that orchards be arranged regularly in quincunxes, the arrangement of spots representing the number five on dice, to take up less room and give better quality produce. The centres of hexagons in a regular hexagonal tiling can be thought of as an elongated quincunx, repeated. As this is essentially the same result used in another context, I’ll give Varro the benefit of the doubt and defer to Varro’s poetic license.)).”
Crimewaves really are waves – but they can be stopped
Nothing puts your home insurance premium up like having been burgled in the past – because it means you’re more likely to be burgled again. Stanford researcher Nancy Rodríguez, with colleagues Henri Berestycki (who is first author, for the record) and Lenya Ryzhik, has developed a travelling waves model to explain this phenomenon – and, more importantly, how to stop it.
Crime, according to past research, tends to cluster in particular neighbourhoods – and even individual houses. Once a crime epicentre has been established, criminal activity tends to spread out in a wave pattern, gradually engulfing larger and larger areas.