Chapter 1

Motivation: Mechanics

and Optics

A mathematical billiard consists of a domain, say, in

billiard table), and a point-mass (a billiard ball) tha

the domain freely. This means that the point moves a

line with a constant speed until it hits the boundary.

off the boundary is elastic and subject to a familiar

of incidence equals the angle of reflection. After the

point continues its free motion with the new velocity u

boundary again, etc.; see figure 1.1.

Figure 1.1. Billiard reflection

An equivalent description of the billiard reflection

impact point, the velocity of the incoming billiard ball

Motivation: Mechanics

and Optics

A mathematical billiard consists of a domain, say, in

billiard table), and a point-mass (a billiard ball) tha

the domain freely. This means that the point moves a

line with a constant speed until it hits the boundary.

off the boundary is elastic and subject to a familiar

of incidence equals the angle of reflection. After the

point continues its free motion with the new velocity u

boundary again, etc.; see figure 1.1.

Figure 1.1. Billiard reflection

An equivalent description of the billiard reflection

impact point, the velocity of the incoming billiard ball