Manchester’s first MathsJam of 2015 (and indeed, all the other first MathsJams of 2015 in cities all over the world) met on 20th January, rousing us all from a Christmas-induced slumber and gently easing us back into a year of recreational maths. Here’s a round-up of what we did.
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Follow Friday: 13/2/15
Remember when we used to do a regular Follow Friday post, recommending mathematically interesting Twitter accounts? Well, this is like that, only not hugely regular. Enjoy it while it lasts!
Carnival of Mathematics 119
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of January, and compiled by Frederick Koh, is now online at White Group Mathematics.
The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.
Puzzlebomb – February 2015
Puzzlebomb is a monthly puzzle compendium. Issue 38 of Puzzlebomb, for February 2015, can be found here:
Puzzlebomb – Issue 38 – February 2015
The solutions to Issue 38 can be found here:
Puzzlebomb – Issue 38 – February 2015 – Solutions
Previous issues of Puzzlebomb, and their solutions, can be found here.
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.)).”
Why Should Penguins Care About Maths?
I regularly review resources written for pupils and teachers that in some way aim to support or extend Science, Technology, Engineering and Mathematics (STEM) education. The most recent campaign in the UK is the Your Life campaign and as usual it has a website with short articles designed for teachers and pupils to browse and be inspired.
Imagine my excitement when one of the articles was called “Why Do Penguins Care About Maths?”. Two of my favourite things together in one article, there was even a video. I imagined something about penguins going North, then East then South on their quest for fish and ending up close to where they started. How does the problem change for a beady-eyed Rockhopper over a majestic (but slightly ridiculous) Emperor? How far does a penguin swim anyway? How do you map three-dimensional movement as it glides up and down under the water? So many possibilities for penguins and maths.
Carnival of Mathematics 118
The next issue of the Carnival of Mathematics, rounding up blog posts from the month of December, and compiled by Andrew Taylor, is now online at AndrewT.net.
The Carnival rounds up maths blog posts from all over the internet, including some from our own Aperiodical. See our Carnival of Mathematics page for more information.