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Re: In "square root of -1", should we say "minus 1" or "negative 1"?
Posted:
Dec 2, 2012 1:19 AM
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On Sat, Dec 1, 2012 at 9:23 PM, Robert Hansen <bob@rsccore.com> wrote:
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> On Dec 1, 2012, at 10:39 PM, kirby urner <kirby.urner@gmail.com> wrote:
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> "Did they teach anything about latitude / longitude when doing coordinate systems with ya? No? What school did you say that was?"
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> https://www.dropbox.com/sh/hz6q14yeafltfmn/Nd3JCDzftM/Freilich-1952.pdf
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> Page 105, 107
>
Yes, though mostly just in passing. When we get to the XY grid and
locating points thereon, the globe is never mentioned.
Coordinate geometry and geography are not strongly linked. "Earth
measure" is for teachers in another subject (STEM was poorly
integrated).
Related reading:
http://education.nationalgeographic.com/education/encyclopedia/prime-meridian/
Did you know anything about US President Chester Arthur before? Soon
after president Garfield who did a proof of the Pythagorean theorem:
http://www.pbs.org/teachers/mathline/concepts/president/activity2.shtm
(web site funded by borrowings from China according to a recent
president wannabe).
The chapter emphasizes directly that positive is to the right and/or
up, negative to the left and/or down (all math is ethno-math). Page
109.
The idea that a number line could be a circle (diurnal time, latitude
etc.) is not explicitly discussed.
When you go east (positive) how do you end up coming back from the
negative side (negative)?
This relates to the issue of Int type numbers that "roll over" from
extreme positive to extreme negative.
Note that reading "-5" as "minus five" and not "negative five" is
explicitly encouraged. Page 106.
There is some mention of clockwise / counterclockwise. There's no
strong initiative to develop handedness as a concept.
There's no mention of an observer or observer position.
Clockwise is relative to an observer. If you look at the same
rotation from 180 opposite side, looking back, it's now
counter-clockwise.
Having directionality depend on the observer is not discussed.
Schoolish math of the 1900s tends to ignore the observer.
No turtle graphics yet :-)
The second number line and a flat grid comes within the chapter, but a
third axis does not.
Space, experientially more real than planar surfaces, will have to
wait. Time too (as its own dimension).
Kirby
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