suddenly telescopes, hundreds of them

telescopes for sale

Yesterday we had a day out at the International Astronomy Show, at the Warwickshire Exhibition Centre, near Leamington Spa. This was a big barn/hanger-like building, with multiple stands from different astronomical kit vendors.  On sale were telescopes, lenses, binoculars, astronomy books and posters, meteorites, plots of land in New Mexico, university courses, small domes, and other astronomically-related things.

more telescopes

a view from the restaurant area, on high

no chance to test any of the kit...

The vibe was a bit like computer shows in their hey-day 30-odd years ago, with crowds of people looking through lots of high tech kit. (The photos here were taken towards the end of the day, when the crowds had thinned. Earlier it was quite a crush.)



It was a typical spring day: cloudy and overcast. However, that didn't stop us buying stuff in anticipation of clear skies later.

We were tempted by the whole sky camera, and the solar telescope, but we eventually just bought a pair of binoculars, in anticipation of comet ISON later this year.

The small comet Panstarrs earlier this year was a bit of a dim, fuzzy disappointment (although some people got spectacular shots of it close to Andromeda).  But we remember the glorious Hale-Bopp from the late 1990s.  So we are getting prepared for later this year with suitable binoculars.  Comet viewing doesn't want a very high magnification, but needs good  light gathering.  So we went for a pair of 15x70.  Let's hope we get those clear skies!

Ironically, we bought the binoculars from Green Witch, our local astronomical supplier, so we could have saved a trip.  (We had previously bough a cardboard solar telescope from them, to watch the 1999 eclipse.  We also bought our proper telescope from them about a decade ago.)

But it was worth going, to see all the different peripherals that are becoming common.  Maybe we'll go for the whole sky camera when the price drops a bit.

sequestering carbon, several books at a time II

This is the catch from Amazon et al over the last fortnight, patiently waiting to be databased:

I'm already about a third of the way through Redshirts, and enjoying it immensely   It seems obvious where it's going, so I'm assuming it will instead go somewhere completely different.

paint the sky with clouds

Walking down to work from the car park this morning, I was greeted by a marvelous sky -- and what appeared to be the cause.

a power station paints the clouds?

Zoom in on the "source", and you can see individual columns of vapour from the several cooling towers of a nearby power station.  The juxtaposition with the clouds makes for a great optical illusion: from this angle, the plume appears to be the source of the entire sky of clouds.

Down the bottom of the path, the view opened out, allowing sight of two more power stations, apparently also painting the sky with clouds.

well, the one on the right hasn't started painting yet, obviously...

food for thought

More than half of the world's population lives inside this circle despite it "being mostly water and including the most sparsely populated country on earth (Mongolia)"

double, double

So there I was, sitting in my study, listening to the rain hammer down, when light suddenly poured in through the window next to me, as the setting sun broke through from under the clouds. Aha!  I grabbed my phone, and dashed to the other side of the house.  And yes, there it was:

A beautiful double rainbow.  (As ever, reality was better than the phone camera could capture.)

And amusingly, the filename of this photo is 20130513_201305.jpg, because the photo was snapped at 13 minutes and 5 seconds past 8pm, on the 13th of May 2013.

trees and flowers

The garden continues to burst into life. Both apple trees are in full bloom.  Given the density of blossom, and the lateness of the season reducing the risk of frost, we're anticipating a bumper crop, or, as we call it, a glut.  There will be many gifts of apples, come autumn.

the old apple tree: tasty cookers

the young apple tree: cruncy Coxes

The acer is looking its healthiest and loveliest since it was planted nearly a decade ago.  It had a few rocky years when we feared we might lose it, but two freezing winters have given it a new lease of life, and it's never looked back.

sunlight through the leaves

It's not just trees springing into life.

more bluebells than any previous year

Worth the long wait!

Mathematical Models

Way back when I was at school, I came across a fascinating little book called Mathematical Models, by Cundy and Rollett.  It had instructions on how to build various mathematical objects, such as stellated polyhedra.  I liked the book so much I actually bought my own copy, new, for £2.95, which was a lot of money back then!

I made a few of the simpler models, but never got much further than the dodecahedron.  I certainly never got as far as making any of the fiddly stellated ones.

So today, when I came across a posting in Google+ about Anselm Levskaya's website polyHédronisme, I was taken right back to those days.  Playing with this interactive web-based systems is much easier than fiddling with card, glue, and scissors, though.  Type in a few commands, and a zoomable, rotatable polyhedron appears!

I've spent my afternoon playing around on this site, and reading up on Conway polyhedron notation that is used to define shapes, and now I can say I have at last "made" some of these polyhedra.

The small stellated dodecahedron is made by raising a pentagonal-based pyramid on every face of a regular dodecahedron. If the pentagons making up the dodecahedron have side length \(1\), then the height of each pyramid should be* \[ \frac{\sqrt{4\sqrt{5}-1}}{2} \approx 1.41\] The Conway notation command in polyHédronisme that achieves this is \(k(5,1.41)D\), which means: start with a dodecahedron \(D\), then raise a pyramid of height \(1.41\) on each \(5\)-sided face.

The great dodecahedron is made by making a pyramidal dimple in every face of a regular icosahedron. If the triangles making up the icosahedron have side length \(1\), then the depth of each pyramid should be* \[ \sqrt{\frac{1}{2}- \frac{\sqrt{5}}{6}} \approx 0.36\] The Conway notation command in polyHédronisme that achieves this is \(k(3,-0.36)I\), which means: start with an icosahedron \(I\), then indent a pyramid of height \(0.36\) on each \(3\)-sided face.

The great stellated dodecahedron is made by raising a pyramid on every face of a regular icosahedron. If the triangles making up the icosahedron have side length \(1\), then the height of each pyramid should be* \[ \sqrt{\frac{7+3\sqrt{5}}{6}} \approx1.51\] The Conway notation command in polyHédronisme that achieves this is \(k(3,1.51)I\), which means: start with an icosahedron \(I\), then raise a pyramid of height \(1.51\) on each \(3\)-sided face.

So much for standard polyhedra.  But polyHédronisme doesn't stop there.  I had great fun playing about with the notation language, producing weird and wonderful forms:

(i)  \(k(20,1)bk(3,2)I\)    (ii)  \(k(12,1)k(10,2)bk(5,1)D\)    (iii)  \(k(20,-0.3)k(6,0.3)bk(3,-0.3)I\)
(iv)  \(k(24,-0.5)k(6,0.2)k(20,-1)bk(3,-0.1)k(5,1)D\)

The results of play can only really be appreciated on the site itself, rotating the polyhedra, and getting a real feel for their shapes, with all their dips and bumps.  A marvellous site.

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* The book Polyhedron Models has helpful stellation diagrams that allow these heights to be calculated, with a little trigonometry.