Biography

Evangelista Torricelli was born in Faenza, part of the Papal States. He was left fatherless at an early age and educated under the care of his uncle, a Camaldolese monk, who first entered young Torricelli into a Jesuit College in 1624 to study mathematics and philosophy until 1626, when he sent Torricelli to Rome in 1627 to study science under the Benedictine Benedetto Castelli, professor of mathematics at the Collegio della Sapienza in Pisa.

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.)

Torricelli died in Florence a few days after having contracted typhoid fever, and was buried in San Lorenzo. The asteroid 7437 Torricelli was named in his honor.

Contributions to Physics

Torricelli's chief invention was the mercury barometer, which arose from solving a practical problem. Pump makers of the Grand Duke of Tuscany attempted to raise water to a height of 12 meters or more, but found that 10 meters was the limit with a suction pump. Torricelli employed mercury, fourteen times more dense than water. In 1643 he created a tube approximately one meter long, sealed at the top, filled it with mercury, and set it vertically into a basin of mercury. The column of mercury fell to about 76 cm, leaving a Torricellian vacuum above. As we now know, the column's height fluctuated with changing atmospheric pressure; this was the first barometer. This discovery perpetuated his fame, and the Torr, a unit used in vacuum measurements, has been named for him.

He also discovered Torricelli's Law, regarding the speed of a fluid flowing out of an opening, which was later shown to be a particular case of Bernoulli's principle. Torricelli's law states that the speed of efflux, v, of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth h is the same as the speed that a body (in this case a drop of water) would acquire in falling freely from a height h , where g is the acceleration due to gravity. This last expression comes from equating the kinetic energy gained, , with the potential energy lost, mgh, and solving for v.

He gave the first scientific description of the cause of wind: "winds are produced by differences of air temperature, and hence density, between two regions of the earth."

Contributions to Geometry

Gabriel's Horn (also called Torricelli's trumpet) is a geometric figure which has infinite surface area but encloses a finite volume. The name refers to the tradition identifying the Archangel Gabriel as the angel who blows the horn to announce Judgment Day, associating the divine, or infinite, with the finite. The properties of this figure were first studied by Italian physicist and mathematician Evangelista Torricelli.

The Fermat point of a triangle is also called Torricelli point, is a point such that the total distance from the three vertices of the triangle to the point is the minimum possible. It is so named because this problem is first raised by Fermat in a private letter. The Fermat point gives a solution to the Steiner tree problem for three points.

This question was proposed by Fermat, as a challenge to Evangelista Torricelli. He solved the problem in a similar way to Fermat's, albeit using intersection of the circumcircles of the three regular triangles instead. His pupil, Viviani, published the solution in 1659.

Achievements

In looking at Torricelli's achievements we should first put his mathematical work into context. Another pupil of Castelli, Bonaventura Cavalieri, held the chair of mathematics at Bologna. Cavalieri presented his theory of indivisibles in Geometria indivisibilis continuorum nova published in 1635. The method was a development of Archimedes' method of exhaustion incorporating Kepler's theory of infinitesimally small geometric quantities. This theory allowed Cavalieri to find, in a simple and rapid way, the area and volume of various geometric figures.

Torricelli studied the methods being proposed by Cavalieri and at first was suspicious of them. However, he soon became convinced that these powerful methods were correct and began to develop them further himself. In fact he used a combination of the new and old methods, using the method of indivisibles to discover his results, but often giving a classical geometrical proof of them. He gave this not because he doubted the correctness of the method of indivisibles, rather because he wanted to give a proof.

By 1641 he had proved a number of impressive results using the methods which he would publish three years later. He examined the three dimensional figures obtained by rotating a regular polygon about an axis of symmetry. Torricelli also computed the area and centre of gravity of the cycloid. His most remarkable results, however, resulted from his extension of Cavalieri's method of indivisibles to cover curved indivisibles.

The Barometer

It was Galileo that suggested Evangelista Torricelli use mercury in his vacuum experiments. Torricelli filled a four-foot long glass tube with mercury and inverted the tube into a dish. Some of the mercury did not escape from the tube and Torricelli observed the vacuum that was created.

Evangelista Torricelli became the first scientist to create a sustained vacuum and to discover the principle of a barometer. Torricelli realized that the variation of the height of the mercury from day to day was caused by changes in the atmospheric pressure. Torricelli built the first mercury barometer around 1644.

Evangelista Torricelli also wrote on the quadrature of the cycloid and conics, the rectifications of the logarithmic spiral, the theory of the barometer, the value of gravity found by observing the motion of two weights connected by a string passing over a fixed pulley, the theory of projectiles and the motion of fluids.

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