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Re: Taxicab Geometry
Posted:
Feb 22, 1995 6:03 PM
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One activity that is interesting is to have students discover what
"shapes" certain loci have in the plane with a taxicab metric. For
example, what "shape" is the "perpendicular bisector" defined by 2 points
(where as a locus, it is defined as the set of points in the plane
equidistant from the two given points). Or what "shape" is a "circle"
(where it is defined as the set of points at a fixed distance from a fixed
point). There are similar questions for each of the other conics, and
indeed for any other loci that are defined in terms of distances.
It's been quite a while since I've looked at Krause (it came out a long
time ago and was only recently brought out in reprint), but I think I
recall that he does not deal with the continuous plane. If that is the
case, you should know that these questions are much more interesting in the
continuous plane. [If I'm wrong in my recollection, ignore this remark.]
If the students have any knowledge of isometries in the Euclidean plane, it
is interesting to have them discover what are the isometries in the plane
with the taxicab metric (which motions are taxicab-distance preserving?).
Doris Schattschneider
At 4:05 PM 2/22/95 -0700, Art Mabbott wrote:
> I hope that someone out there can provide me with some help. I am
>working my way through the small paperback book "Taxicab Geometry - An
>Adventure in Non-Euclidean Geometry" by Eugene F. Krause with a topics
>class of high school pre-math anal jrs and srs. And I would like to pick
>the brains of those who have used it before. What I'd like is a summative
>type activity to evaluate and access. This could be in the form of a
>paper, project, test, or whatever has worked for you. We are trying to
>focus on writing across the entire curriculum and they have done some
>"mathematically meaningful writing" so it could be a written. But it
>doesn't have to be...
>
> At Newport, we in the math department have defined mathematically
>meaningful writing as (in correct paragraph form) 1) state and explain the
>problem, 2) explain your process (including any false starts), 3) state
>any conclusions and/or answers and justify them (Why are they the right
>answers? Are there other less correct answers?), 4) reflect on what your
>learned and what you did, and finally 5) prepare it like a 5-star
>restaurant would prepare a meal-with class.
>
>Art Mabbott
>******************************************************************************
> mabbotta@belnet.bellevue.k12.wa.us
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