Re: [Edu-sig] turtle coordinates: Y increase downards - as in most graphics API?
From: kirby urner <kirby.urner@gmail.com>
Regarding coordinate systems, I'm probably the only teacher to use what I call Quadrays in the classroom. ... ... I tell them this is what Martians use, acknowledging this is purely science fiction,
Kirby, Looking way far in the back of my head, the closest thing (to the inspirational drawings of your notebook) I could recover is what is called fundamental lattice structures of solid state physics. Not sure, but in there they might use your coordinate system to better describe structures of crystals. The book by Kittel, pg 27 of the 8th Edition, has some stuff on it. Other object in that sense is the Quaternion thing https://en.wikipedia.org/wiki/Quaternion Better stop here, I am getting hurt ... Sergio Check out the free first draft of the book: Prealgebra via Python Programming https://www.researchgate.net/publication/325473565 https://github.com/rojassergio/Prealgebra-via-Python-Programming ---------------------------------------------------------------------- Message: 1 Date: Tue, 19 Jun 2018 09:05:50 -0700 From: kirby urner <kirby.urner@gmail.com> To: "edu-sig@python.org" <edu-sig@python.org> Subject: Re: [Edu-sig] turtle coordinates: Y increase downards - as in most graphics API? Message-ID: <CAPJgG3Qn_oLs5LFhznrdv-25K51xB=Y8gf-zrj6Xid=aPnitiQ@mail.gmail.com> Content-Type: text/plain; charset="utf-8" On Tue, Jun 19, 2018 at 7:27 AM, Sergio Rojas <sergio_r@mail.com> wrote:
Some issues to keep in mind:
From the The Feynman Lectures on Physics:
http://www.feynmanlectures.caltech.edu/I_52.html[http://www.feynmanlectures.caltech.edu/I_52.html] """ Fig. 52?1(b)! The first molecule, the one that comes from the living thing, is called L-alanine. The other one, which is the same chemically, in that it has the same kinds of atoms and the same connections of the atoms, is a ?right-hand? molecule, compared with the ?left-hand? L-alanine, and it is called D-alanine. ... ... So it looks as though the phenomena of life permit a distinction between "right" and "left," ... """
?Yes, a very excellent suggestion and apropos in this context, Sergio. The Feynman piece is fascinating. I like that he features a "Martian" (see below). Congruent vs. Chiral: I hang out on some math teacher web groups (mostly on Facebook) and one topic that comes up a lot is "congruence". Interestingly, the math concept of "congruence" teaches us to overlook or ignore "chirality" or handedness in structures, despite these enantiomers having completely different chemical properties.? We would say the left hand is congruent to the right hand in a math class. I downloaded the PDF of your book and am reading it. Impressive! Mixing math and programming and deriving the benefits of synergy has been one of my themes as well. Regarding coordinate systems, I'm probably the only teacher to use what I call Quadrays in the classroom. Indeed, next week I'll be sharing a summer camp course in "Martian Math" with some Silicon Forest kids that features this alternative coordinate system, with four basis rays from the center of a regular tetrahedron to its four corners, using positive 4-tuples. All points in space are linear combinations of these four basis vectors. I have Python code for converting back and forth to XYZ. The centers of closest packed spheres in the CCP all have positive whole number coordinates. https://en.wikipedia.org/wiki/Quadray_coordinates[https://en.wikipedia.org/wiki/Quadray_coordinates] https://github.com/4dsolutions/Python5/blob/master/Generating%20the%20FCC.ip... I tell them this is what Martians use, acknowledging this is purely science fiction, and suggest that comparing and contrasting a conventional apparatus with something alien (unfamiliar) actually helps students achieve a deeper understanding of the convention. Martians also use triangles and tetrahedrons to model 2nd and 3rd powering such that 3 x 3 x 3 is a tetrahedron of 27, not a cube of 27. We have a constant for going back and forth between XYZ cubic volumes and IVM tetra volumes. http://www.4dsolutions.net/satacad/martianmath/toc.html[http://www.4dsolutions.net/satacad/martianmath/toc.html] (from my previous iteration of this class)
Other Related links: https://phys.org/news/2014-10-handedness-life.html[https://phys.org/news/2014-10-handedness-life.html] http://www.iflscience.com/space/why-life-left-handed-answer-stars/[http://www.iflscience.com/space/why-life-left-handed-answer-stars/]
?Yes very useful. Looking for chemical signatures in space leads me to Harold Kroto's discovery of C60 and its subsequent analysis and synthesis as a topic. https://youtu.be/yZ8JDDnyxC4[https://youtu.be/yZ8JDDnyxC4] (another link re chirality) Thanks again! Kirby ?
Sergio Check out the free first draft of the book: Prealgebra via Python Programming https://www.researchgate.net/publication/325473565[https://www.researchgate.net/publication/325473565] https://github.com/rojassergio/Prealgebra-via-Python-Programming[https://github.com/rojassergio/Prealgebra-via-Python-Programming] _______________________________________________
Hi Sergio -- Thanks for taking a look at the Q-ray coordinates! You're right about many bridges to crystallography in this neighborhood. I'm part of a tiny subculture that came up with Q-rays in a listserv long ago. http://mathforum.org/library/view/6236.html It's not that I'm the only one familiar with the ideas or that I'm the only contributor, just I know of no one else bringing it to the attention of a pre-college class, and I do that only rarely. The connection with Python is a Quadray class is implemented therein. My friend Tom has them in C++ (see Wikipedia). https://github.com/4dsolutions/Python5/blob/master/QuadraysJN.ipynb I've also dabbled in a Clojure version. https://github.com/4dsolutions/synmods/blob/master/qrays.clj I worked with Quaternions a long time ago, to do a rotating cube applet, but then applets became a deprecated technology, much to everyone's surprise and consternation. http://4dsolutions.net/ocn/oopalgebra.html Kirby On Tue, Jun 19, 2018 at 12:14 PM, Sergio Rojas <sergio_r@mail.com> wrote:
Kirby,
Looking way far in the back of my head, the closest thing (to the inspirational drawings of your notebook) I could recover is what is called fundamental lattice structures of solid state physics. Not sure, but in there they might use your coordinate system to better describe structures of crystals. The book by Kittel, pg 27 of the 8th Edition, has some stuff on it.
Other object in that sense is the Quaternion thing https://en.wikipedia.org/wiki/Quaternion
Better stop here, I am getting hurt ...
Sergio
participants (2)
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kirby urner -
Sergio Rojas