**Evangelista Torricelli** (

October 15,

1608 -

October 25,

1647) was an

Italian physicist and

mathematician.

Born in Faenza , he was left fatherless at an early age. He was educated under the care of his uncle, a Camaldolese monk, who in 1627 sent him to Rome to study science under the Benedictine Benedetto Castelli (1577-1644), professor of mathematics at the Collegio della Sapienza in Pisa. Torricelli died a few days after having contracted typhoid fever.

## Torricelli's work in physics

The perusal of Galileo's Two New Sciences (1638) inspired him with many developments of the mechanical principles there set forth, which he embodied in a treatise *De motu* (printed amongst his *Opera geometrica*, 1644). Its communication by Castelli to Galileo in 1641, with a proposal that Torricelli should reside with him, led to Torricelli repairing to Florence, where he met Galileo, and acted as his amanuensis during the three remaining months of his life.

After Galileo's death Torricelli was nominated grand-ducal mathematician and professor of mathematics in the Florentine academy . The discovery of the principle of the barometer which has perpetuated his fame ("Torricellian tube", "Torricellian vacuum") was made in 1643. The torr, a unit of pressure is named after him.

## Torricelli's work in mathematics

Torricelli is also famous for the discovery of an infinitely long solid now called *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, who tried several alternative proofs), and prompted a fierce controversy about the nature of infinity, involving the philosopher Hobbes. It is supposed by some to have led to the idea of a "completed infinity".

Torricelli was also a pioneer in the area of infinite series. In his *De dimensione parabolae* of 1644, Toricelli considered a decreasing sequence of positive terms and showed the corresponding telescoping series necessarily converges to *a*_{0} - *L*, where *L* is the limit of the sequence, and in this way gives a proof of the formula for the sum of a geometric series.

## References

Weil, André, *Prehistory of the Zeta-Function*, in Number Theory, Trace Formulas and Discrete Groups, Aubert, Bombieri and Goldfeld, eds., Academic Press, 1989

Last updated: 10-29-2005 02:13:46