16007[EMHL] Re: A metric theorem on choo-choos

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• Jan 9, 2008
Dear Francois,

[FR]
Of course this configuration is well known.
Looking at the position of the choo-choos at time t = 0 and time t =
1, we get 3 pairs:
(a(0), a(1)) on side BC, (b(0), b(1)) on side CA, (c(0), c(1) on side
AB. Hence we obtain 3 direct similarities:
1° Sa of center <alpha> sending the pair (b(0), b(1)) on the pair
(c(0),c(1))
2° Sb of center <beta> sending the pair (c(0), c(1)) on the pair
(a(0),a(1))
3° Sc of center <gamma> sending the pair (a(0), a(1)) on the pair
(b(0),b(1))

-----

I considered the points a(0), b(0) and c(0) as the train engines and
the points a(1), b(1) and c(1) as the train brake vans. With segments
a(0)a(1), b(0)b(1) and c(0)c(1) taken as the trains, I was pleased to
see the invariance of your points T and S as the segment trains moved
along their respective sidelines. This prompted my comment about the
trains not needing uniform motion.

Sincerely, Jeff
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