[Edu-sig] turtle coordinates: Y increase downards - as in most graphics API?

Tue Jun 19 15:14:11 EDT 2018

From: kirby urner <kirby.urner at 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

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Message: 1
Date: Tue, 19 Jun 2018 09:05:50 -0700
From: kirby urner <kirby.urner at gmail.com>
To: "edu-sig at python.org" <edu-sig at python.org>
Subject: Re: [Edu-sig] turtle coordinates: Y increase downards - as in
most graphics API?
Message-ID:
<CAPJgG3Qn_oLs5LFhznrdv-25K51xB=Y8gf-zrj6Xid=aPnitiQ at mail.gmail.com>
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On Tue, Jun 19, 2018 at 7:27 AM, Sergio Rojas <sergio_r at 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.ipynb

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]
> _______________________________________________
>
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Message: 2
Date: Tue, 19 Jun 2018 10:29:46 -0700
From: Yoshiki Ohshima <Yoshiki.Ohshima at acm.org>
To: "edu-sig at python.org" <edu-sig at python.org>
Subject: Re: [Edu-sig] turtle coordinates: Y increase downards - as in
most graphics API?
Message-ID:
<CAHC3jCO86eF_PKfJQ0hdmrWD++vo-E2ZSnBqdnTeHi-M2xvtdg at mail.gmail.com>
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I also stick my nose here.

The notion of "in computer graphics Y goes down" is not as true as some
people think. The graphics you are looking at right now on your computer
most likely to have gone through some programs that use "Y goes up" scheme
(such as GLSL).

Only if you are talking about pixels and raster graphics, you could say
that there is a dominant convention to make Y go down, but in with vectors,
there is no such dominance.

For end-users, why does it matter how actually pixels are stored in the
actual memory? Computer is medium that can simulate anything; so the
decision should not be based on what computer does at the lower levels.

Once we leave from what computer does at low-level, there are math text
books, which are dominantly "Y-up". Why do they have to know two different
conventions? Unless, of course, learning the fact that the coordinate
system is just a convention and can be different.

Also there may be a case where the particular turtle graphics
implementation is tied to the lower level pixel representation. But is
basically mixing different abstraction levels, and unless you want to teach
about mixing abstraction levels, it is a bad starting point.

In summary: the statement "in computer graphics Y goes down" is a wrong
argument for turtle graphics to use Y-down coordinate system. Then, for
turtles and for end-users, there is an existing convention to make Y go
down. So that should be a better default.

On Mon, Jun 18, 2018 at 9:54 AM, Kevin Cole <
kevin.cole at novawebdevelopment.org> wrote:

> Sticking my nose in where it don't belong. ;-) But that's never stopped me
> before. ;-)
>
> First "I are not a teacher". At least, not in any formal sense of the
> word. Second, some would say "I are not a programmer". I don't listen to
> those people.
>
> In spite of the common "in computer graphics Y goes down", does that make
> sense to new learners? I've gotten used to various coordinate systems, but
> the first time I had to work with graph paper and plotting (and, for that
> matter, maps) one goes "up" ("north", "forward") for Y. Then again, maybe
> the average learner isn't quite as flexible these days, and telling them
> after they've gotten used to a system that they have to flip everything
> upside down and backwards isn't a great idea. I attribute my own
> flexibility not to any innate ability but rather to learning during a time
> when architectures OS's and languages were changing fast enough that there
> wasn't time to become set in one's ways.
>
> ?[Note: Grammatical "mistakes" above are meant as weak -- very weak --
> humor. At least, most are.]?
> --
> *Kevin Cole*
> <http://novawebdevelopment.org[http://novawebdevelopment.org]>
> NOVA Web Development Co-Op
> http://novawebdevelopment.org/[http://novawebdevelopment.org/]
> Arlington, VA
>
> _______________________________________________
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>

--
-- Yoshiki
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