A page of a calendar is partially covered by the previous torn sheet (see the figure). The vertices A and B of the upper sheet lie on the sides of the bottom sheet. The fourth vertex of the lower leaf is not visible – it is covered by the top sheet. The upper and lower pages, of course, are identical in size to each other. Which part of the lower page is greater, that which is covered or that which is not?
The population of China is one billion people. It would seem that on a map of China with a scale of 1 : 1,000,000 (1 cm : 10 km), it would be possible to fit a million times fewer people than there is in the whole country. However, in fact, not only 1000, but even 100 people will not be able to be placed on this map. Can you explain this contradiction?