of collisions is
(1.3)
[
^r—l
I arctan y 777,1/7712 I
Exercise 1.3. Extend the upper bound on the numb
to a wedge convex inside; see figure 1.4.
Figur e 1.4. A plane wedge, convex inside
Exercise 1.4. a) Interpret the system of two point-m
ment, subject to elastic collisions with each other and
points of the segment, as a billiard.
b) Show that the system of three point-masses 777,1,7
line, subject to elastic collisions with each other, is iso
billiard inside a wedge in three-dimensional space. P
dihedral angle of this wedge is equal to
(1.4) arctan [ 777,2 \ I
V V 777,1777,2777,3 /
c) Choose the system of reference at the center of ma
the above system to the billiard inside a plane angle (
d) Investigate the system of three elastic point-masses o
1.1. Digression. Billiard computes TT. Formula
possible to compute the first decimal digits of TT. Wh
brief account of G. Galperin's article [39].
Consider two point-masses on the half-line and ass
100fc777,i.
Let the first point be at rest and give the se
the left. Denote by N(k) the total number of collisions
in this system, finite by the above discussion. The cla
N(k) = 3141592653589793238462643383..
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