A classic Pythagoras

After devoting more than half a century to riddles, I have concluded that the best school for the development of ingenuity is mathematics and mechanics. I have witnessed the development of brilliant minds that began solving puzzles and when a fan of problem solving tells me that he is going to present himself to this or that exam or work, I know he will succeed for sure. Instead, I sometimes observe how some university studies are anti-ingenuity and all they do is incapacitate students for their professions.

The kindergarten of teaching seeks to fascinate its students and is based on the fundamental law that the mind should not be filled with memorized rules, but that what is explained must be done clearly, so that the student can formulate his own rules. Mathematics has always been loaded with too many rude, dark and heavy rules, that very few understand what they mean. So, when they finish their studies, most forget about them, glad they never have to remember them again.

When a principle is truly understood, that difficulty no longer exists. Even calculations called abstruse are still sums or multiplications. Put we multiply 888,888 x 777,777. It will take us much longer, but it is as easy as multiplying 8 x 7. We will only find a complex sum difficult if we are not well acquainted with the mechanism of addition.

All these mathematical mechanisms can be taught through a puzzle. We can inject a little fun into the riddle and teach how to cultivate and also appreciate humor. The problem should be dressed in a way that is accessible and thus easier to understand. It is fine if we base the problem on a mechanical truth, on some historical event or on some classical wisdom that also contributes to improving the knowledge of the person who reads it, because when we learn this way, we store small pieces of information that are never forgotten.

2400 years ago, Pythagoras discovered that if he drew squares on the three sides of a right triangle, the longest square would have exactly the same area as the two smaller ones together. Pythagoras was so exultant with the theme that the larger square was always equal to the two little ones, regardless of the dimensions of the triangle, that he offered all his possessions to the gods, but they laughed at him and told him to walk to explain His discovery to dogs.

Take a piece of paper of the dimensions of the 2 squares as shown in the illustration and cut it into three pieces that fit perfectly to form a square.

Solution

Here is the solution. The figure on the left shows how to make the cuts and the one on the right how we should place the pieces so that they fit together forming a square: