When you saw us outside building snow-mathematicians and throwing snowballs we weren't just larking about, honestly! We were actually conducting in-depth research into symmetry and trajectories — and here our results are behind door number 2...
Everyone knows what symmetry is, and the ability to spot it seems to be hard-wired into our brains. Mario Livio explains how the symmetry we admire in a snow flake might also explain the workings of the Universe.
Through the looking-glass
When Alice stepped through the looking glass in Lewis Carroll's Through the Looking-Glass and What Alice Found There, she would have found that more than just the writing was back to front. The very molecules that made up her body would have been the wrong way around in the looking-glass world, and their
interaction with the looking-glass molecules would have led to a very confusing — and possibly dangerous — adventure!
Oh the weather outside is frightful,
But the fire is so delightful,
And since we've no place to go,
Let It Snow! Let It Snow! Let It Snow!
How seasonal! The first day of our Plus Advent Calendar and the country is blanketed by snow! Admittedly the Plus team also has a broken boiler and children home due to school closure, but we do love the snow!
So to celebrate the frosty beginning of December, we have hidden all things icy behind Door #1. Wrap up warm, pack a thermos of hot tea and strap on your skis and enjoy!
A molecule's eye view of water
Water is essential for life on Earth, and it is a resource we all take for granted. Yet it has many surprising properties that have baffled scientists for centuries. Seemingly simple ideas such as how water freezes are not understood because of water's unique properties. Now scientists are utilising increased computer power and novel algorithms to accurately simulate the properties of water on the nanoscale, allowing complex structures of hundreds or thousands of molecules to be seen and understood.
Maths and climate change: the melting Arctic
The Arctic ice cap is melting fast and the consequences are grim. Mathematical modelling is key to predicting how much longer the ice will be around and assessing the impact of an ice free Arctic on the rest of the planet. Plus spoke to Peter Wadhams from the Polar Ocean Physics Group at the University of Cambridge to get a glimpse of the group's work.
Teacher package: On thin ice - maths and climate change in the Arctic
On the 1st of March 2009 three intrepid polar explorers, Pen Hadow, Ann Daniels and Martin Hartley, set out on foot on a gruelling trip across the Arctic ice cap to conduct the Catlin Arctic Survey. In this teacher package we look at some of the maths and science behind their expedition — climate and sea ice models, GPS and cartography, and how to present statistical evidence.
What are continued fractions? How can they tell us what is the most irrational number? What are they good for and what unexpected properties do they possess? Where are they in the Universe and just what does chaos have to do with it?
To get you in the festive spirit Science in School is offering you an advent calendar with a difference — no little doors to open, no pictures of snowmen and no chocolate. Instead, each day for 24 days, they will send you an email with an inspiring teaching idea. Perhaps a science game to play at the end of term, maybe a fun experiment, some fascinating science facts, links to particularly good websites, or a beautiful picture to use in lessons.
Students are invited to submit a poster designed to convey the essence of a mathematical topic that has been covered by their university course to AS and A level students. You can submit a poster either as an individual, as a group, or as part as your course. The deadline is the 31st of March 2011 and the prize consists of £100 plus you'll have an A2 version of your poster printed and sent out to schools. Each printed poster will
prominently feature the name(s) of its designer(s) together with recognition of their
universities, Rolls-Royce plc and the FMSP. You can see winning designs of previous years here.
The best posters will be:
attractively laid out
capable of enriching a course in AS or A level mathematics
likely to attract school/college students to take mathematics (or mathematics-related
subjects) at university
Posters may be designed in any readily available software. Ideally, the page layout should be
set to 59.4cm × 42.0cm, using either landscape or portrait format. The university’s logo
should appear in the top left corner and there should be a space 7cm high x 5cm wide in the
top right corner for the FMSP logo. The bottom 2cm of the poster should be left blank. All
images should be at least 300dpi.
The poster designs must be the students’ original work and you will be required
to sign a declaration that this is the case. No image used should be protected by copyright.
Entries may be submitted by students studying in any university department.
The FMSP reserves the right to edit the winning
design before printing to ensure that it is technically correct and complete. Winners may be
required to contribute actively to the editing process.
Entries should be submitted by e-mail to RichardBrowne@furthermaths.org.uk by 31 March
2011. The email must include the name(s) and full contact details of the designer(s). The
poster design should be attached to the e-mail, in the form of an editable file.
The dramatic curved surfaces of some of the iconic buildings created in the last decade, such as 30 St Mary's Axe (AKA the Gherkin) in London, are only logistically and economically possible thanks to mathematics. Curved panels of glass or other material are expensive to manufacture and to fit. Surprisingly, the curved surface of the Gherkin has been created almost entirely out of flat panels of glass — the only curved piece is the cap on the very top of the building. And simple geometry is all that is required to understand how.
One way of approximating a curved surface using flat panels is using the concept of geodesic domes and surfaces. A geodesic is just a line between two points that follows the shortest possible distance — on the earth the geodesic lines are great circles, such as the lines of longitude or the routes aircraft use for long distances. A geodesic dome is created from a lattice of geodesics that intersect to cover the curved surface with triangles. The mathematician Buckminster Fuller perfected the mathematical ideas behind geodesic domes and hoped that their properties — greater strength and space for minimum weight — might be the future of housing.
To try to build a sphere out of flat panels, such as a geodesic sphere, you first need to imagine an icosahedron (a polyhedron made up of 20 faces that are equilateral triangles) sitting just inside your sphere, so that the points of the icosahedron just touch the sphere's surface. An icosahedron, with its relatively large flat sides, isn't going to fool anyone into thinking it's curved. You need to use smaller flat panels and a lot more of them.
Divide each edge of the icosahedron in half, and join the points, dividing each of the icosahedron's faces into 4 smaller triangles. Projecting the vertices of these triangles onto the sphere (pushing them out a little til they two just touch the sphere's surface) now gives you a polyhedron with 80 triangular faces (which are no longer equilateral triangles) that gives a much more convincing approximation of the curved surface of the sphere. You can carry on in this way, dividing the edges in half and creating more triangular faces, until the surface made up of flat triangles is as close to a curved surface as you would like.