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
"""
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://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 (from my previous iteration of this class)

Other Related links:
https://phys.org/news/2014-10-handedness-life.html
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 (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://github.com/rojassergio/Prealgebra-via-Python-Programming

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