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Tuesday, 24 April 2018  |  Paul Stephenson

We use the same language to describe uniform tilings and polyhedra: Platonic if all the regular polygons are the same, Archimedean if there's a mixture, and a tiling - like the kagome pattern, 3.6.3.6 - can be thought of as an infinite polyhedron. What controls the size of the polyhedron is the angular defect, d, the difference from 360°, at each vertex. They total 720°, so, if there are v vertices, vd = 720°.

Monday, 23 April 2018  |  Paul Stephenson

In the case of our own planet the story begins around 4.3 billion years ago with the appearance of solid matter: ions joining to form crystals. We have to jump forward the same amount of time before organic life had evolved with the sophistication to discover their structures. Right up until the middle of the twentieth century this evidence was still indirect: we observed the scattering pattern when samples were bombarded by X-rays. But the electron microscope and its successors enabled us to identify individual ions. An important two-dimensional pattern discovered among minerals is the subject of this piece.

Tuesday, 4 July 2017  |  Admin
Tuesday, 4 July 2017  |  Admin

In order to test out some challenge activities I went to a local High School to run the first activity with a lower ability Year 8 class.

Tuesday, 30 May 2017  |  Paul Stephenson

An unmarked regular tetrahedron has planes of symmetry. It does not therefore have left- and right-handed forms. (The technical word for handedness is chirality.) But here are nets for two tetrahedra in which each face has a different colour.

1 CommentMonday, 13 March 2017  |  Admin

As part of the London Schools Excellence Fund, The Compton School in partnership with Finchley Catholic High School recently held two maths masterclasses for strong Year 6 mathematicians from schools in the Barnet and Haringey areas. They were ably supported by Year 8 students from the The Compton and Year 9 students from Finchley Catholic.

Tuesday, 14 February 2017  |  Paul Stephenson

Most Sudoku puzzles use the numbers 1 to 9, but you can use anything – letters, colours, shapes, …And you can make up puzzles with fewer items. We shall use just 4. If you think such puzzles are likely to be too simple, I warn you that we shall move from 'single' Sudoku to 'double' Sudoku and even 'triple double' Sudoku.

Tuesday, 14 February 2017  |  Paul Stephenson

Having built a polyhedron from a net or illustration, students will feel pleased with what they have done. But they can now capitalise on their success by finding the properties of their shape. Most important are the planes of mirror symmetry and axes of rotation symmetry. Then there is the matter of how many faces, edges and vertices they have. It is this second question which concerns us here.

Tuesday, 14 February 2017  |  Paul Stephenson

The 4 Colour Map Theorem says that you never need more than 4 colours to colour a map so that regions with the same colour don’t touch. You have to count the region round the edge because the theorem is really about a map drawn on a sphere. The theorem is shape-blind. It doesn’t matter what shape a region is. What matters are the regions it shares a border with.

Friday, 10 February 2017  |  Admin

I am the Teaching and Learning Adviser for Maths and Numeracy for Jersey in the Channel Islands. Having purchased some Polydron for delivering some class based reasoning activities, I started to wonder about the possibility of running an interschool competition where the rounds of the competition are hands on construction activities with Polydron.


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