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))

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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