2 1. DEFORMATIONS

Problem 1.2. A pretzel ha s two holes tha t "hold " a doughnu t (se e Fig-

ure 1.2 (a)). Show that th e pretzel can be deformed i n such a way that one

of its "handles" will unlink itsel f fro m th e doughnut (Figur e 1.2 (b)).

(a) (b )

FIGURE 1.2

Problem 1.3. A circle is drawn on a pretzel with two holes (Figure 1.3 (a)).

Show that it is possible to deform th e pretzel so that the circle will be in the

position represented in Figure 1.3 (b).

(a)

FIGURE 1.3

Problem 1.4. Sho w that a punctured tube from a bicycle tire can be turned

inside out. (Mor e precisely, this would be possible if the rubber fro m whic h

the tub e i s made wer e elasti c enough . I n real lif e i t is impossible t o turn a

punctured tub e inside out.)