## 32. Siesta

Albert lay lazily on the sun-drenched terrace, drifting into a sweet doze. This did not prevent him, however, from observing his right hand. "My index and middle fingers," he thought, "form an angle of about $20^{\circ}$. Can I, while keeping their relative position, turn my hand so that the shadows of my fingers are perpendicular to each other?" A minute later, having found the answer to his question, he sighed contentedly—and fell asleep immediately.

Could you, in his place, fall asleep just as quickly?
32. Albert placed the tips of his index and middle fingers on the terrace (a horizontal plane), maintaining a constant angle between them ($20^{\circ}$). When his hand rotates around these two points of support, the angle formed by the shadows of his fingers changes: it is $20^{\circ}$ when the hand lies on the terrace, and $180^{\circ}$ when the hand lies in a plane parallel to the sun's rays. Since this change in angle occurs continuously, at some point the two shadows will form exactly a right angle ($90^{\circ}$ is between $20^{\circ}$ and $180^{\circ}$). This conclusion is simple enough that, were we in Albert's place, we too would quickly fall asleep.