Thorn Cycles Forum
Community => Non-Thorn Related => Topic started by: in4 on May 31, 2013, 12:34:26 PM
-
Olympic cycling etc. from the Open University; for all the helmet wearers amongst us! ;)
http://www8.open.ac.uk/choose/ou/engagement-cycling?ONEML=enq44p&MEDIA=enq44prp_eml12
-
Great stuff! OU's a great source for all sorts of things -- thanks.
Didn't hear the word "fun" intrude, though, as in, "Are we having fun yet?" Or, "C'est pas fun." Nor "beauty". But then, I was looking only at vid #2 -- will check the others.
J.
-
The OU DVDs I have for Maths (M208) digitized from videos from the 80s crack me up every time.
The geek is ueberstrong in them.
OU is great BTW I am doing a part-time BSC in computing and maths with them. No way I could do it w/o the flexibility OU offers.
-
Most people in the UK, and elsewhere that the Freeview channels are available by satellite (and in the States via PBS), owe at least part of their further/adult education to the Open University, often without realizing they're being educated. Many, many of the programmes on BBC TV channels Three and Four in science, history, social commentary, literature, drama even, cosmology, physics, art, all kinds of interesting stuff, is in fact OU materials. Watch the credits at the end, and you'll discover you've been watching the most entertaining study materials ever made.
Andre Jute
-
Most people in the UK, .... owe at least part of their further/adult education to the Open University
Andre Jute
So true. I left school without any formal qualifications and the OU educated me (I was one of the early students, watching science experiments on a B&W tv). Then in the early 1980s I managed to get a job as a BBC producer making ..... TV programmes for the OU. Although we had moved on to colour by then. And then came the video cassette!! Wow - now our lives would change forever. Once we had the video cassette we could do all sorts of things that were just not possible with broadcast tv.
I got to meet and make programmes with some amazing people - including a young James Dyson in his workshop - where he had made over 2,000 models of a cyclone (in brass) in order to perfect his crazy idea for a bag-less vacuum cleaner. (I also got to interview the marketing manager of a major vacuum cleaner company who said it would never catch on).
But one of the highlights was to work with a team from the University of Nebraska (and Kansas) in the early 1990s on an international project for first year undergrads across the globe, called The Bicycle in Science, Technology and Society. They included some big names from the world of bicycle science, (e.g. David Gordon Wilson and Chester Kyle) and although they got some US and EU funding, the project staggered as is often the way with these things when those with the money could not understand how you could use something as simple as a bicycle to teach some fundamental physics and materials science. The simplicity and accessibility of the bicycle to educators (particularly those outside the US and UK) was lost on them.
I'm long since retired from those days, but I was lucky - the OU not only educated me - it also gave me a wonderful job.
ian
-
That's a wonderful anecdote, and CV, Ian!
Andre Jute
-
OU is a great institution--one of the UK's outstanding contributions to adult education and citizenship. I'm privileged to know a couple of people who have taught with OU -- and now, at a distance, Jawine and Ian too. Well done to you both!
J.
-
I found a bicycle wheel excellent to illustrate Group Theory (symmetry groups) and specifically elements g in group G that are Generators, eg repeat application of their group operation (f.e. rotation) creates G.
Leaving aside logos etc. a bikewheel with 36 spokes is more or less symmetrical on rotation. With 18 spokes on each side, each spoke rotated by 2PI/18 can be place in the position of all the other spokes and thereby on rotation can "generate" the whole wheel.
Is that snoring from the back of the lecture theater?
:P
-
I like thinking about symmetry groups and bicycle wheels!
But I am not so sure about 2 * pi / 18!
If the wheel is laced radially, that seems right. But if the wheel is laced tangentially, then half the 18 go off the hub clockwise and the other half go counter-clockwise. So maybe 2 * pi / 9 is closer.
The fun thing, too, is that one can flip the wheel over. So it seems like a group with two generators, one of order 2 and one of order 9.
-
Really small things amuse great minds. -- 101 Things Albert Einstein Never Said
-
Nods wheel lacing comes into play.
Pedantry alert: An element g of group G is a generator if g has the order of G.
So you can't have order 2 and order 9 generators for the same wheel.
I guess you meant you need to rotate either 2 or 9 times?
Hobbes Einstein wasn't easily amused, was he? :P
-
Hobbes Einstein wasn't easily amused, was he? :P
Truth is, I don't know. But I wouldn't be surprised if dear old Albert had a good sense of humor. Otherwise, how did he stay sane for forty years while he searched for and failed to find the Grand Unified Theory?
But I'll distract you with another piece of trivia: Karl Marx, a most ugly man, was very successful with women because he had such a good sense of humor. Absolutely true, and verifiable.
Andre Jute
-
I think the total group is a product of two subgroups, one of order 2 and one of order 9. The order 2 subgroup is where you flip the wheel. I guess that only works on front wheels... that don't have disk brakes!
Gets me thinking about wheels where the two sides aren't laced the same. Of course rear wheels are most commonly dished. But, .e.g. the torque on the rear wheel always goes the same way... maybe one could have 24 spokes taking that torque and only 12 to pull the other way?
Shakespeare always had that follow through punch line, e.g. "and fools seldom differ!" Maybe Einstein did too. Perhaps too kind to say it though!
-
Ha! Group theory!
Suppose a*a = 1 and b**9 = 1. In a commutative group.
Then (ab)*9 = a. It's looking like ab is actually a generator! (ab)*10 = a*b*(ab)**9 = a * b * a = b.
So one can generate the whole symmetry group of a 36 spoke tangentially laced wheel with the generator that flips the wheel over and rotates 1/9 of the circle. Two such moves should put the wheel back in the first orientation but rotated 2/9 of the circle.
Rusty gears up there. Regular lubrication has been neglected!
-
OK so a is self-inverse (as a*a = 1 which is e in multiplication)
Ah b is a wheel flip. We got taught a generator must be just one element, that keeps getting repeated.
So a wheel flip + rotation wouldn't be "legal" in math speak ;)
I had to ignore quite a bit of things to get it to work maybe we need a wagon wheel :D
-
I was thinking of "a" as a wheel flip.
(http://i140.photobucket.com/albums/r6/kukulaj/Nomad/spokes_zps1cbc74b5.jpg)
Looking closely at my rear wheel, this is how the spokes look. Spokes 1 and 3 are hooked to the near flange of the hub, 2 and 4 to the far flange. Flipping the wheel around the dashed line will take 1 to where 4 is and 2 to where 3 is... making the picture look just the same, so it is a symmetry. And of course flipping twice is like not flipping at all, i.e. a*a = 1.
b is a rotation, taking one cluster of 4 spokes around to the next cluster of 4 spokes. On a 36 spoke hub, there will be 9 clusters, and rotating through all 9 is a 360 degree rotation, i.e. no rotation at all, so b**9 is 1.
a*b is really a single element of the group - you can multiply elements together any which way, and the result is always just some other element. Of course, some of the elements might get a bit more difficult to think about or describe than others! So in this case, a*b is a flip then rotate. That is still a symmetry operation and a member of the group.
What's curious to me is that a*b seems to be a generator of the group for a 36 spoke wheel... but not for a 32 spoke wheel! If b**8=1, then (a*b)**8 is just 1. There need to be an odd number of 4 spoke clusters for there to be a generator of the group!
All this got me to take a closer look at the spoke pattern on my wheels!
-
I am starting to think that some of the people on here have a little too much time on their hands.
This is the kind of thing that happens when your bike gets too reliable and you can't find anything that needs tweeking
LOL
Andy
-
Ah OK I see what you mean now, flip twice and we are back to Wheel One. (instead of Square one, that's {e,a,b,c} direct with {r,s,t,v} :P
It gets worse with fancy spoke patterns...what's wrong with tricross ;D
Have you heard of the Counting Theorem to calculate how many possible symmetries you can make? Eg I have a cube, and I have two colors to paint it with, how many can I make w/o making the same cube?
http://en.wikipedia.org/wiki/Burnside%27s_lemma
Group theory is great fun. For me at least. Me and Analysis don't really get on atm.
Exam 18 June...M208.
Lol Andy I was building up a vintage Ciocc, well am, stretching tubulars as we speak. Only time now cos I hunted down all the parts :D
-
Exam 18 June...M208.
Good luck. Don't let those groupies back you into a corner. You got them surrounded in your wheel.
Andre Jute
-
Ooops, this wheel symmetry group is not commutative! So my blathering about a*b being a generator, that is totally bogus.
a*b*a*b = 1 because if you flip the wheel, rotate a bit clockwise, flip it again, then rotate again a bit clockwise... the two rotations just cancel each other out!
Yeah, good luck on your exam! Don't make the silly mistakes that I do!
-
Exams you get set questions...no surprises ;)
What's purple and commutes...
...an Abelian Grape.
I'll get my Moebius coat, except I'm not sure what side to put it on.