Niccolo Fontana Tartaglia

Niccolò Fontana (Brescia, c. 1499 - Venice, December 13, 1557) was an Italian mathematician and engineer, nicknamed Tartaglia because of his stuttering.

Biography

He was born in Brescia in 1499, a city then dependent on the Republic of Venice. He was the son of Michele Fontana, who died when Tartaglia was six years old, leaving the family, mother and three children, in a situation of poverty.

When he was twelve years old, French troops under the command of Gastón de Foix invaded the city of Brescia. Niccolò Fontana, despite being hidden in the cathedral, received several wounds to his face and jaw, one of them to his mouth. The consequences of this injury caused him to stutter, which gave rise to the nickname Tartaglia (stammerer) with which he came to sign his works.

Orphaned and without the material means to provide himself with formal instruction, Tartaglia is said to have only learned half of the alphabet (exactly up to the letter k) from a private tutor before the money ran out, and subsequently had to learn the rest on your own. Be that as it may, learning from him was essentially self-taught.

He became one of the leading mathematicians of the 16th century. In 1535, he spread the rumor that he had discovered the formula for solving quadratic equations. Antonio Maria Del Fiore, a disciple of the mathematical professor at the University of Bologna Scipione del Ferro, raised his voice in protest and accused tartaglia of being an impostor, to elucidate this situation Fiore challenged Tartaglia to a contest. Tartaglia accepted and won the challenge. He taught this science successively in Verona, Vicenza, Brescia, and finally, in Venice; where he died in 1557 victim of material poverty, which accompanied him throughout his life.

Contributions to classical algebra

He was the inventor of a method, similar to the formula for quadratic equations, for solving quadratic equations. While already in Venice, in 1535, his colleague del Fiore (a disciple of Scipione del Ferro, from whom he had received the formula for solving cubic equations), proposed a mathematical duel, which Tartaglia accepted. From this duel and in his eagerness to win it, Tartaglia developed the general formula to solve the equations of the third degree, for which he was able to solve the thirty questions that his opponent raised, without his being able to solve any of the proposals by Tartaglia., which had drawn on his own work begun five years earlier, when Zuanne da Coi had asked him to solve two cubic equations of a type Del Fiore was unable to solve.

Tartaglia's success in the duel reached the ears of Gerolamo Cardano, who begged him to communicate his formula, to which he agreed, but requiring Cardano to swear not to publish it. However, in view of the fact that Tartaglia did not publish his formula, and that an unpublished writing by another mathematician dated before Tartaglia's was apparently in the hands of Cardano, and in which the same result was reached independently, it was finally Cardano who Considering himself free from the oath, he published it in his work Ars magna (1545). Despite the fact that Cardano credited Tartaglia with authorship, he was deeply affected, going so far as to publicly insult Cardano, both personally and professionally, ending up being irreconcilable enemies. As a consequence of these facts, Tartaglia's formulas passed to posterity as Cardano's formulas.

Other notable contributions by Tartaglia were the first studies on the application of mathematics to artillery in calculating the trajectories of projectiles (work later confirmed by studies on the fall of bodies carried out by Galileo), as well as by the mathematical expression for calculating the volume of any tetrahedron based on the lengths of its sides, the so-called Tartaglia formula, a generalization of Heron's formula (used to calculate the area of the triangle):

V2=1288det[chuckles]0d122d132d1421d2120d232d2421d312d3220d3421d412d422d4320111110]{display} V^{2}{2}{2}{1}{1}{2}{1⁄2}{2}{2}{2}{2}{2}{1}{2}{2}{2}}{2}{2}{2}{2}{2}{1⁄2}{2}{2}{2}{1⁄2}{2}{2}{2}{1⁄2}{1⁄2}{1⁄2}{2}{1⁄2}{2}{1⁄2}{2}{2}{2}{2}{1⁄2}{2}{2}{2}{2}{1⁄2}{2}{1⁄2}{1⁄2}{1}{1⁄2}{1}{1}{1⁄2}{1}{1⁄2}{1}{1}{1}{1}{1}{1⁄2}{2}{1⁄2}{1⁄2}{1⁄2}{1⁄2}{1}{1}{

. In addition to his mathematical works, Tartaglia published the first Italian translations of the works of Archimedes and Euclid.

Works

General trattato de' numeri et misure, 1556

Questi et invenzioni diverse of Niccolò Tartaglia

• Trattato di numeri et misure.
• Nuova Scientia, cioè invenzione nuovamente trovata utile per ciascuno speculativo matematico bombrdero et altri (1546).
• Questi et invenzioni diverse.
• Travagliata invenzione.
• Trattato di arithmetic.

He also dedicated himself to writing books, in total he wrote 43 books.