Evangelista Torricelli (nonfiction)

Portrait of Evangelista Torricelli by Lorenzo Lippi circa 1647.

Evangelista Torricelli (15 October 1608 – 25 October 1647) was an Italian physicist and mathematician, best known for his invention of the barometer, but is also known for his advances in optics and work on the method of indivisibles.

His father was a textile worker and the family was very poor. Seeing his talents, his parents sent him to be educated in Faenza, under the care of his uncle, Jacobo, a Camaldolese monk, who first ensured that his nephew was given a sound basic education. He then entered young Torricelli into a Jesuit College in 1624, possibly the one in Faenza itself, to study mathematics and philosophy until 1626, by which time his father, Gaspare, had died. The uncle then sent Torricelli to Rome to study science under the Benedictine monk Benedetto Castelli, professor of mathematics at the Collegio della Sapienza (now known as the Sapienza University of Rome). Castelli was a student of Galileo Galilei. "Benedetto Castelli made experiments on running water (1628), and he was entrusted by Pope Urban VIII with hydraulic undertakings." There is no actual evidence that Torricelli was enrolled at the university; nonetheless it is almost certain that Torricelli was taught by Castelli. In exchange he worked for him as his secretary from 1626 to 1632 as a private arrangement. Because of this, Torricelli was exposed to experiments funded by Pope Urban VIII.

While living in Rome, Torricelli became also the student of the brilliant mathematician, Bonaventura Cavalieri, with whom he became great friends. It was in Rome that Torricelli also became friends with two other students of Castelli, Raffaello Magiotti and Antonio Nardi. Galileo referred to Torricelli, Magiotti, and Nardi affectionately as his "triumvirate" in Rome.

In 1632, shortly after the publication of Galileo's Dialogues of the New Science, Torricelli wrote to Galileo of reading it "with the delight [...] of one who, having already practiced all of geometry most diligently [...] and having studied Ptolemy and seen almost everything of Tycho Brahe, Kepler and Longomontanus, finally, forced by the many congruences, came to adhere to Copernicus, and was a Galileian in profession and sect". (The Vatican condemned Galileo in June 1633, and this was the only known occasion on which Torricelli openly declared himself to hold the Copernican view.)

Aside from several letters, little is known of Torricelli's activities in the years between 1632 and 1641, when Castelli sent Torricelli's monograph of the path of projectiles to Galileo, then a prisoner in his villa at Arcetri. Although Galileo promptly invited Torricelli to visit, Torricelli did not arrive until October 10, 1641, just three months before Galileo's death. The reason for this was that Torricelli's mother, Caterina Angetti died. "(T)his short intercourse with the great mathematician enabled Torricelli to finish the fifth dialogue under the personal direction of its author; it was published by Viviani, another pupil of Galileo, in 1674."

After Galileo's death on 8 January 1642, Grand Duke Ferdinando II de' Medici asked him to succeed Galileo as the grand-ducal mathematician and chair of mathematics at the University of Pisa. In this role he solved some of the great mathematical problems of the day, such as finding a cycloid's area and center of gravity. As a result of this study, he wrote the book the Opera Geometrica in which he described his dobservations. The book was published in 1644. Little was known about Torricelli in regard to his works in geometry when he accepted the honorable position, but after he published Opera Geometrica two years later, he became highly esteemed in that discipline. "He was interested in Optics, and invented a method whereby microscopic lenses might be made of glass which could be easily melted in a lamp." As a result, he designed and built a number of telescopes and simple microscopes; several large lenses, engraved with his name, are still preserved in Florence.

Torricelli studied projectiles and how they traveled through the air. "Perhaps his most notable achievement in the field of projectiles was to establish for the first time the idea of an envelope: projectiles sent out at [...] the same speed in all directions trace out parabolas which are all tangent to a common paraboloid. This envelope became known as the parabola di sicurezza (safety parabola)."

Torricelli is also famous for the discovery of the Torricelli's trumpet (also - perhaps more often - known as Gabriel's Horn) whose surface area is infinite, but whose volume is finite. This was seen as an "incredible" paradox by many at the time, including Torricelli himself, and prompted a fierce controversy about the nature of infinity, also involving the philosopher Hobbes. It is supposed by some to have led to the idea of a "completed infinity". Torricelli tried several alternative proofs, attempting to prove that its surface area was also finite - all of which failed.

Torricelli was also a pioneer in the area of infinite series. In his De dimensione parabolae of 1644, Torricelli considered a decreasing sequence of positive terms, giving a proof of the formula for the sum of a geometric series.

Torricelli developed further the method of indivisibles of Bonaventura Cavalieri. Many 17th century mathematicians learned of the method through Torricelli whose writing was more accessible than Cavalieri's.

On 11 June 1644, he famously wrote in a letter to Michelangelo Ricci:

Noi viviamo sommersi nel fondo d'un pelago d'aria. (We live submerged at the bottom of an ocean of air.)

Fiction cross-reference

• Crimes against physics
• Gnomon algorithm
• Mathematics

Nonfiction cross-reference

• Galileo Galilei (nonfiction)
• Christen Sørensen Longomontanus (nonfiction)
• Mathematics (nonfiction)
• Blaise Pascal (nonfiction)
• Physics (nonfiction)
• Michelangelo Ricci (nonfiction)
• Vincenzo Viviani (nonfiction)

External links:

• Evangelista Torriceli @ Wikipedia