Mathematics in Literature

1. In the famous European fairy tale Cinderella by the Charles Perrault, the magic ends precisely at midnight (12:00 at night). If we look at the dial of a clock as a complete circle of 360°, what geometric angle do the hour hand and the minute hand form exactly at 12:00?

2. In the German fairy tale Rapunzel by the Brothers Grimm, the princess lets her long hair hang out of the window of the tower so that the prince can climb up. If the tower is perpendicular to the ground (90°) and we know the height of the window (a) and the distance from the base of the tower to the prince's horse (b), what famous geometric theorem helps us calculate the minimum length of the hair stretched out (c)?

3. In the Danish fairy tale Thumbelina by Hans Christian Andersen, the little heroine rides a lily pad floating on water. If the pad is a perfect circle with radius R, what is the universal mathematical formula we use to calculate the area of ​​the surface on which Thumbelina can stand?

4. In the fairy tale The Town Musicians of Bremen by the Brothers Grimm, four animals (a donkey, a dog, a cat, and a rooster) climb one behind the other to scare off robbers. If the order in which they stand matters, in how many different ways (permutations) can the 4 animals be arranged to form a vertical tower?