Unscheduled Post: The Silver Ratio

May 20, 2009

John Cook on The Endeavour has just mentioned the wonderful silver ratio. As this is probably my favourite number I can’t resist the chance to put up some pictures. The silver ratio: \Psi = 1+\sqrt{2}, is as John mentions the value of the continued fraction with just 2′s, it is also the larger solution of the equation \Psi^2 - 2 \Psi - 1 = 0. This goes directly into its geometric interpretations, as the diameter of an octagon and the size of a rectangle that gives a smaller version of itself when you remove two squares:

Oct_and_rect

Geometric interpretations of the Silver Ratio.

In terms of tiling the golden ratio of course has the Penrose tiling, with its five fold rotational symmetry, the silver ratio plays the same role for the Ammann-Beenker tiling, with 8-fold rotational symmetry:

Ammann_Scaling_bb

Version of my Ammann-scaling artwork

In fact if you find things with 8-fold rotation (Islamic art for example) the silver ratio will be lurking around. I have a personal theory that the silver ratio was as much in Christopher Wren‘s work as the golden. I have not studied it in depth, the floor under the great dome of St. Paul’s has an giant octagon. Anyone know any good studies that might mention this, it would be good to have evidence!

Silver_circles

7 Comments | Art, Mathematics, Unscheduled Post | Tagged: , , , , , , , , , , , , | Permalink
Posted by gelada

How do shapes fill space?

May 17, 2009

One of my main activities at the moment is making toys and materials for an interactive tilings and geometry exhibit at the this year’s Royal Society Summer Science Exhibition.  The title is above. Lots of fun but also hard work. As I recently sent the flyer to the printer I thought it was a good time to annouce it here. So, if you are in London, why not visit us there from the 30th of June to the 4th of July.

The exhibit tells some of the story of tiling from ancient patterns through to hyperbolic and 4d geometry. You get to play with shapes and geometric toys and look at models and pictures. There will even be plenty of maths for those who insist.
flyer_3b

Leave a Comment » | Art, Main Article, Mathematics | Tagged: , , , , , , , , , , | Permalink
Posted by gelada

WoW 7: The secret life of numbers

May 14, 2009

Numbers are one hell of a powerful idea, and some idea of them seems to predate a lot of other intelligence traits. Even young chicks have some ability to count. (this story was a great reverse April fool, true even though it hit the news on April the first). With the internet we can see for the first time how numbers get used. The secret lives of numbers is a fascinating visualisation of this data, though it is getting a little long in the tooth. Maybe its time to automate this and take weekly accounts from google, giving a detailed history of numbers as well as direct comparison.

Frequencies of the first million numbers

Frequencies of the first million numbers

Maxwell Demon: Website of the week

I am handing out awards, the imaginatively titled “Maxwell’s Demon” website of the week:

wowThere is even a prize, £50.  Though I am lazy so the conditions of this are that the winner:

1) Realises they have won.

2) Contacts me.

3) Puts the logo on their site.

Of course 3 is hard to enforce so you could probably take the money and remove the graphical mess.  I will therefore claim that 3 is to ensure that you are indeed the winner.

Leave a Comment » | Art, Mathematics, Website of the week | Tagged: , , , , | Permalink
Posted by gelada

Interesting Manhole covers

May 9, 2009

Its been a busy week workwise, and so a slow week as far as the blog is concerned. So I give you some easily missed art.  This is a job I would love, if anyone can hook me up: designing unusual manhole covers.  There is something very appealing about having your work under everyones nose but usually unoticed.  Waiting for someones casual interest to turn into a wonderful discovery.  Here are three from my recent trip to Vestmannaeyjar in Iceland.  The Puffin street sign they have are a bit too cutesy though.

Just irregular enough to make my brain try to parse writing.

Just irregular enough to make my brain try to parse writing.

Geometric flower

Geometric flower

Apollonian Gasket? Why must there be Tarmac over both of these I found, why why why?

Apollonian Gasket? Why must there be Tarmac over both of these I found, why why why?

6 Comments | Art, General, Main Article | Tagged: , , , , , | Permalink
Posted by gelada

« Previous Entries
Follow

Get every new post delivered to your Inbox.

Join 213 other followers