A square pond with a big tree growing on each corner, someone wants to double the pond area and still be square without affecting the growth of the big tree.

Analysis: Let these four big trees be at the midpoint of each side of the expanded square pond, which is equivalent to taking the side length of the original square as the hypotenuse of four isosceles right triangles.

Solution: It is possible to turn the trees at these four corners into the midpoints of four sides, as shown in the following figure:

Comments: The key consideration of this question is that the square cannot be expanded according to the original angle, but after changing the angle, it can be expanded again. There are green lotus leaves floating on the clear water of the small pond, and the lotus leaves are holding

blooming lotus flowers, just like the smiling face of a little girl.

Little fish in twos and threes are swimming around under the lotus leaf, as if they are playing hide-and-seek.

Lovely frogs are jumping around on the lotus leaf, as if practicing long jump.

Hard-working little dragonflies are flying around the small pond, busy catching mosquitoes.

beautiful small pond, happy world.

There are flower beds around the pond, which contain all kinds of beautiful flowers and many trees like umbrellas. These colorful flowers and tall trees make the small pond extraordinarily beautiful.

The water in the pond is clear and green, and it is as calm as a mirror. All kinds of fish live here, some are golden, some are red, some are black and white ... These fish swim freely in the water every day and live a very happy life. Even the tortoise and the frog have settled down here ...

I often go to the pond to play and watch the fish swimming for more than an hour. Usually, I will bring some bread and steamed bread residue to feed them, and it is really interesting to watch them swim in droves and scramble for food!

One day, I went to the pond to play again, and found that the pond was different: there were all kinds of packaging bags, beverage bottles and some petals and branches floating on the water ... It was really terrible. I really hate those people who litter. I really want to say to them, "didn't you hear the cries of fish, frogs and little turtles for help?" Please don't destroy the environment and return the happy homes of those little people, okay? "