Folha: 'Squaring the circle, synonymous with impossible'

Reproduction of Marcelo Viana's column in Folha de S. Paulo. The question dates back to classical Greece and is quite simple to formulate: to construct, using only a ruler and compass, a square whose area is equal to that of a given circle. But centuries of failed attempts made "squaring the circle" synonymous with an impossible problem, even before the German Ferdinand von Lindemann (1852–1939) gave, in 1882, a mathematical demonstration that such a construction does not exist – which definitively settled the matter. Definitively? How good it would be if it were that simple! But I will return to this point… The Greek playwright Aristophanes (446–386 BC) already referred to squaring the circle with undisguised irony. In the comedy "The Birds," premiered in 414 BC, some citizens of Athens, tired of the hectic life of the capital, decide to found a city in the air and emigrate to it. Pistetero, the protagonist, is exasperated by architects and urban planners who offer unsolicited services. "Good heavens, who are you?" he asks. "I am Melon, known throughout Greece," replies the other. "And what is this?" asks Pistetero. "A ruler for measuring the air. The contour of the air is like an oven. Applying the ruler here and the compass there… Do you understand?" explains Melon. "Nothing!" retorts Pistetero. Melon tries: "With this ruler I draw a straight line, inscribe a square in the circle and place the square in the center. All the streets flow to it, in the same way that straight rays emanate from the center of a star in all directions." "By the gods, this man is a true Thales!" reacts Pistetero, sarcastically comparing the scoundrel to Thales of Miletus, the first Greek mathematician. Read more: IMPA develops algorithm to optimize oil extraction Lectures and computer science classes mark PIC PAPMEM meetings will be held between January 27 and 31 The Roman philosopher Anicius Boethius (480–524) was another infected by the "morbus cyclometricus , " as the "virus" of squaring the circle was jokingly called. Boethius was born in Rome a few years after the deposition of the last emperor of the West, Romulus Augustulus. The name had pedigree: Romulus was the mythical founder and first king of Rome, and Augustus was the first emperor. But in Latin the suffix "ulus" indicates diminutive: nothing expresses more eloquently the extent to which the once powerful Rome had declined than the fact that its last ruler was called Romulus Augustinus. Boethius then lived under the reign of Theodoric the Great (474–526), the Ostrogothic leader who conquered and ruled the Italian peninsula. He was a senator, consul, and even head of government. He wrote works on philosophy, theology, and history, and his translations of the Greek classics were crucial in preserving Aristotle's ideas for posterity. In "Liber circuli," he stated that he had solved the squaring of the circle "but the demonstration is too long to be reproduced here in its entirety." An expression that Pierre de Fermat (1601–1665) would make famous in similar circumstances, more than a millennium later. However, in the Frenchman's case, the theorem was true and was eventually proven by Andrew Wiles (b. 1953) at the end of the 20th century. Boethius, on the other hand, was condemned to death, tortured, and executed by order of Theodoric. But it seems this was for suspected treason, not for having stated false theorems. To read the full article, visit the newspaper's website. Also read: IMPA Tech is accepting applications until December 27th. Folha: 'QR code: what is it, where does it come from, and where is it going?'