Niccolò Fontana Tartaglia

Niccolò Fontana Tartaglia
Niccolò Fontana Tartaglia.

Niccolò Fontana Tartaglia (1499/1500, Brescia – 13 December 1557, Venice) was a mathematician, an engineer (designing fortifications), a surveyor (of topography, seeking the best means of defense or offense) and a bookkeeper from the then-Republic of Venice (now part of Italy). He published many books, including the first Italian translations of Archimedes and Euclid, and an acclaimed compilation of mathematics. Tartaglia was the first to apply mathematics to the investigation of the paths of cannonballs; his work was later validated by Galileo's studies on falling bodies. He also published a treatise on retrieving sunken ships.

Niccolò Fontana was the son of Michele Fontana, a rider and deliverer. In 1505, Michele was murdered and Niccolo, his two siblings, and his mother were impoverished. Niccolò experienced further tragedy in 1512 when the French invaded Brescia during the War of the League of Cambrai. The militia of Brescia defended their city for seven days. When the French finally broke through, they took their revenge by massacring the inhabitants of Brescia. By the end of battle, over 45,000 residents were killed. During the massacre, a French soldier sliced Niccolò's jaw and palate with a saber. This made it impossible for Niccolò to speak normally, prompting the nickname "Tartaglia" ("stammerer").

There is a story that Tartaglia learned only half the alphabet from a private tutor before funds ran out, and he had to learn the rest for himself. Be that as it may, he was essentially self-taught. He and his contemporaries, working outside the academies, were responsible for the spread of classic works in modern languages among the educated middle class.

His edition of Euclid in 1543, the first translation of the Elements into any modern European language, was especially significant. For two centuries Euclid had been taught from two Latin translations taken from an Arabic source; these contained errors in Book V, the Eudoxian theory of proportion, which rendered it unusable. Tartaglia's edition was based on Zamberti's Latin translation of an uncorrupted Greek text, and rendered Book V correctly. He also wrote the first modern and useful commentary on the theory. Later, the theory was an essential tool for Galileo, just as it had been for Archimedes.

Contents

Solution to cubic equations

Tartaglia is perhaps best known today for his conflicts with Gerolamo Cardano. Cardano cajoled Tartaglia into revealing his solution to the cubic equations, by promising not to publish them. Several years later, Cardano happened to see unpublished work by Scipione del Ferro who independently came up with the same solution as Tartaglia. As the unpublished work was dated before Tartaglia's, Cardano decided his promise could be broken and included Tartaglia's solution in his next publication. Even though Cardano credited his discovery, Tartaglia was extremely upset. He responded by publicly insulting Cardano.

Volume of a tetrahedron

Tartaglia is also known for having given an expression (Tartaglia's formula) for the volume of a tetrahedron (incl. any irregular tetrahedra) as the Cayley–Menger determinant of the distance values measured pairwise between its four corners:

 V^2 = \frac{1}{288} \det \begin{bmatrix} 
  0 & d_{12}^2 & d_{13}^2 & d_{14}^2 & 1 \\
d_{21}^2 & 0   & d_{23}^2 & d_{24}^2 & 1 \\
d_{31}^2 & d_{32}^2 & 0   & d_{34}^2 & 1 \\
d_{41}^2 & d_{42}^2 & d_{43}^2 &   0 & 1 \\
  1 &   1 &   1 &   1 & 0
\end{bmatrix}

where d ij is the distance between vertices i and j. This is a generalization of Heron's formula for the area of a triangle.

Triangle

Tartaglia is known for having devised a method to obtain binomial coefficients called Tartaglia's Triangle (also called Pascal's Triangle).

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  • Niccolo Fontana Tartaglia — Niccolò Fontana Tartaglia [nik:o lɔ fon ta:na tar ta:ʎ:a] (* 1499 oder 1500 in Brescia, Italien; † 13. Dezember 1557 in Venedig) war ein venetianischer Politiker und Mathematiker …   Deutsch Wikipedia

  • Niccolò Fontana Tartaglia — Niccolo Fontana Tartaglia Niccolò Fontana Tartaglia [nik:o lɔ fon ta:na tar ta:ʎ:a] (* 1499 oder 1500 in Brescia, Italien; † 13. Dezember 1557 in Venedig) war ein venetianischer Politiker und Mathematiker …   Deutsch Wikipedia

  • Niccolo Fontana Tartaglia — Niccolò Fontana Tartaglia Niccolò Fontana dit Tartaglia (« Le Bègue »), né à Brescia en 1499 et décédé à Venise en 1557, est un mathématicien italien. Niccolò Fontana est issu d une famille pauvre. Lors de la prise de Brescia par les… …   Wikipédia en Français

  • Niccolò Fontana Tartaglia — Niccolò Fontana (1500 13 de diciembre de 1557), matemático italiano apodado Tartaglia (el tartamudo) desde que de niño recibió una herida en la toma de su ciudad natal, Brescia, por Gastón de Foix. Huérfano y sin medios mater …   Wikipedia Español

  • Niccolò Fontana Tartaglia — Niccolo Fontana (1500 13 de diciembre 1577), matemático italiano apodado Tartaglia (el tartamudo) desde que de niño recibiera una herida en la toma de su ciudad natal, Brescia, por Gastón de Foix. Huérfano y sin medios materiales para proveerse… …   Enciclopedia Universal

  • Niccolo Fontana — Tartaglia Niccolò Fontana Tartaglia [nik:o lɔ fon ta:na tar ta:ʎ:a] (* 1499 oder 1500 in Brescia, Italien; † 13. Dezember 1557 in Venedig) war ein venetianischer Politiker und Mathematiker …   Deutsch Wikipedia

  • Niccolò Fontana — Niccolo Fontana Tartaglia Niccolò Fontana Tartaglia [nik:o lɔ fon ta:na tar ta:ʎ:a] (* 1499 oder 1500 in Brescia, Italien; † 13. Dezember 1557 in Venedig) war ein venetianischer Politiker und Mathematiker …   Deutsch Wikipedia

  • Niccolo Fontana — Tartaglia Niccolò Fontana Tartaglia Niccolò Fontana dit Tartaglia (« Le Bègue »), né à Brescia en 1499 et décédé à Venise en 1557, est un mathématicien italien. Niccolò Fontana est issu d une famille pauvre. Lors de la prise de Brescia… …   Wikipédia en Français

  • Tartaglia, Niccolò Fontana — ▪ Italian mathematician Tartaglia also spelled  Tartalea   born 1499, Brescia, republic of Venice [Italy] died Dec. 13, 1557, Venice       Italian mathematician who originated the science of ballistics.       During the French sack of Brescia… …   Universalium

  • Tartaglia, Niccolò Fontana, llamado — ► (1500 77) Matemático italiano. Se le debe la resolución algebraica de la ecuación de tercer grado y la aplicación de las matemáticas a la artillería …   Enciclopedia Universal

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