# The Royal Path to Mathematics

"I am forced to tell you again, your Imperial Highness, that the Royal road to geometry has not yet been invented!" Euclid exclaimed annoyed to King Ptolemy when he saw that he had fallen asleep in the middle of one of his geometry lessons. .

“To illustrate the futility of teaching trying to put boring lessons on sticks in your head,” said Beppo, the court jester, “I volunteer to make a few observations to add a little salt to this topic.

“My dear and enlightened friend has been talking about six geometric figures, the trapeze, the square, the Greek cross, the parallelogram - or diamond - the rectangle and the right triangle. The trapeze, as we have been told, is a geometric shape with six sides, none of which are parallel. This form originated many years ago as a mainsail of a catamaran. The other five figures can immediately be recognized as flags and badges of old ships.

“Well, the most interesting thing about this topic is that I can divide this trapeze into five parts, which will form six wonderful puzzles. If we cut those five pieces on paper, it won't be easy to put them back together to form the trapeze. Try using those five pieces to form a perfect square. They also fit perfectly to form a Greek cross and if they continue playing they will also form a parallelogram, a rectangle or a right triangle.

“Thus, we have the six geometric figures formed by those five magic pieces. And I assure you that by the time you have figured out how to assemble the six puzzles, you will have become perfectly familiar with the six forms without having had to give up on sleep by rolling up the eleven volumes of Euclid.

“To reproduce the figures, the five figures should always be used, as with the trapeze. With these exercises we will enter into the knowledge of the mystical affinity between the different geometric figures, as the ancient philosophers saw it. ”

#### Solution

These are the geometric figures that can be formed with the five pieces of the sentence: