I figured out how to find them, it was fairly easy. I just used a quaternion rotation matrix and rotated about the known vertices according to the known rotation symmetry of a cuboctahedron and did this a few times, generating new vertices, and all was well. I also wrote one of the coordinates...
*note - this is not a homework problem.
I have the locations of three vertices of a regular cuboctahedron with edges of unit length (all vertices are length 1 from the center).
They are (1,0,0), (1/2, sqrt(3)/2, 0), (1/2, sqrt(3)/6, sqrt(2)/2)
or in spherical coordinates (1, 0, pi/2)...
Yes. Thinking in terms of operators / vector spaces is really what is new to me. Now that I am starting to connect the dots, the vector space approach is starting to make more sense to me, which is good, because quantum mechanics seems to make explicit use of it.
Ahh. That is about as lucid a tie in from quaternions to vector space as I could ask for. I am going to actually write that down in my notebook and keep it in mind, as I am studying vector spaces now (Hermitian operators, pauli spin matrices, etc.) and keep wondering what the specific...
Not too complex? Explain that nicely?
The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next - by Lee Smolin
Agree or disagree, it really is a perspective that is worth reading, comprehending, and considering.
Certainly there has been much work done on the Clifford algebras, the algebras in general, hypercomplex numbers, etc. but I have never really seen a single publication dedicated to quaternionic analysis as I have real and complex analysis. I wasn't aware of the term 'noncommutative analysis'...
Well, once you all become mathematicians, could you please create Quaternion Analysis, (and hey, go for Cayley/Graves/Octonion Analysis if you are feeling really brave) because Complex Analysis is just not cutting it. Us folks really need you mathematicians to help us out on this one.
After beginning studies in the mathematics of quantum mechanics, this is what I am starting to notice. I prefer quaternions, though I noticed that the way non-commutative operators have been used with pairs of complex numbers is basically the same thing, as you said. It would seem to me to be...
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Hi Peter,
I sympathize, and share your interest for Nottale's theory. I do believe that it is a worthwhile path of study, and am open to any specific critiques of the theory, as it is indeed a work in progress - though I find it more promising than the alternatives at the moment. I...
A great idea - though members might want to consider not recreating entries needlessly that are explained well in wikipedia. It's not hard to find endless arrays of physical and mathematical concepts explained there.
In am one who has a very low post count, but has signed up for a subscription. The reason I have a low post count is simply that I am a relatively new formal student of physics, and wish to learn more before I enter into serious conversations about many of the subjects I am interested in, as I...
Well, either which way - I'm glad your forum is getting recognition, I hope your work is rewarded Mr. Bernhardt.
Now to the forum -
May the conversations be lively.
Well, I was on the fence about it - as I would rather a slightly more technical (but not painfully so) magazine - but I think this will push me over. I might as well just get it. Thanks for informing us!
This text is from the Wikipedia entry - Speed of Light
http://en.wikipedia.org/wiki/Speed_of_light
I had just read it earlier today, and thought of it when I read your post.
"Faster-than-light" observations and experiments
Main article: Faster-than-light
The blue glow in this "swimming...