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[[Image:Niccolò Tartaglia.jpg|thumb|180px|Niccolò Fontana Tartaglia.]]
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'''Niccolò Fontana Tartaglia''' ({{IPA-it|nikkoˈlɔ fonˈtana tarˈtaʎʎa}}; 1499/1500, [[Brescia]] &ndash; 13 December 1557, [[Venice]]) was an Italian [[mathematician]], [[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, known as [[ballistics]], in his [[Nova Scientia]], “A New Science;” his work was later validated by [[Galileo Galilei|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"), which he adopted.
 
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 classical works in modern languages among the educated middle class.
 
His edition of [[Euclid]] in 1543, the first translation of the ''[[Euclid's Elements|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 [[Eudoxus of Cnidus|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]].
 
However, his best known work is his treatise ''General Trattato di numeri, et misure'' published in Venice 1556&ndash;1560. This has been called the ''best'' treatise on [[arithmetic]] that appeared in the sixteenth century.<ref>{{harvnb|Smith|1985|loc=pg. 298}}</ref> Not only does Tartaglia have complete discussions of numerical operations and the commercial rules used by Italian arithmeticians in this work, but he also discusses the life of the people, the customs of merchants and the efforts made to improve arithmetic in the 16<sup>th</sup> century.
 
==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 equation]]s, by promising not to publish them. Tartaglia divulged the secrets of the solutions of three different forms of the cubic equation in verse.<ref>{{harvnb|Katz|1998|loc=pg. 359}}</ref> 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. Mathematical historians now credit both with the paternity of the formula to solve cubic equations, referring to it as the "Cardano-Tartaglia Formula".
 
==Volume of a tetrahedron==
{{Main|Tetrahedron#Volume}}
 
Tartaglia is also known for having given an expression ('''Tartaglia's formula''') for the [[volume]] of a [[tetrahedron]] (including any irregular tetrahedra) as the [[Cayley–Menger determinant]] of the [[Distance|distance values]] measured pairwise between its four corners:
 
:<math> 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} </math>
 
where ''d''<sub>&nbsp;''ij''</sub> is the distance between vertices ''i'' and&nbsp;''j''. This is a generalization of [[Heron's formula]] for the area of a [[triangle]].
 
==Notes==
{{reflist}}
 
==References==
* {{citation|first=Victor J.|last=Katz|title=A History of Mathematics: An Introduction|edition=2nd|year=1998|publisher=Addison Wesley Longman|place=Reading|isbn=0-321-01618-1}}
 
* {{citation|first=D.E.|last=Smith|title=History of Mathematics|volume=I|publisher=Dover Publications|place= New York|year=1958|isbn=0-486-20429-4}}
 
==External links==
* {{MacTutor Biography|id=Tartaglia}}
*[http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=1345&bodyId=1491 Tartaglia's work (and poetry) on the solution of the Cubic Equation] at [http://mathdl.maa.org/convergence/1/ Convergence]
*{{CathEncy|wstitle=Nicolò Tartaglia}}
*[http://galileo.rice.edu/Catalog/NewFiles/tartalia.html The Galileo Project]
*[http://www.historytoday.com/dunia-garcia-ontiveros/treasures-london-library-unlucky-genius?utm_source=History+Today&utm_campaign=9e6b4941f7-weekly_0306&utm_medium=email History Today]
 
{{Use dmy dates|date=September 2010}}
 
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              =Tartaglia, Niccolo Fontana
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = Italian mathematician and engineer
| DATE OF BIRTH    =
| PLACE OF BIRTH    =
| DATE OF DEATH    = 1557
| PLACE OF DEATH    =
}}
{{DEFAULTSORT:Tartaglia, Niccolo Fontana}}
[[Category:15th-century births]]
[[Category:1557 deaths]]
[[Category:Ballistics experts]]
[[Category:People from Brescia]]
[[Category:16th-century Italian mathematicians]]
[[Category:Italian engineers]]
[[Category:Italian military engineers]]

Revision as of 15:41, 26 February 2014

The U.S. automaker - the third largest advetiser in the united states, established a report from the Wall Street Journal. A source knowledgeable about the automaker's plans said GM's advertising professionals decided Facebook's ads had little impact on people.



The ideal situation is that the connection performance (i.e. print ad, TV commercial, radio spot, promotion's directions, online contests, etc.) reveals a great balance between items capabilities versus certain problem-solving potential while still being distinctive. It is very important to maintain a definite focus on your competitive advantage. Be brief. Remember that when you say too much you lose your audience's interest.

The Witches' Market is one of the oddest areas in South America. The market is in the previous quarter of La Paz. It has certainly become an attraction for curious visitors, selling from llama fetuses, dry frogs to countless talismans and potions.

Nonetheless, allis well that ends well. The sycophant was recently placed on a longterm, that is of indefinite duration, leave of absence. The current promotion's style, channel and meaning will soon be changing soon.

The grade of your audio recording is extremely important. A poor audio-recording gives the impression that you're unprofessional. This can reflect poorly upon your product and on you. You could actually lose a lot of income just because of low quality audio-recording.

This Really Is another frequent costeffective Ad Agency idea that it is possible to surely reap the benefits of. Produce a few prints of one's company and whether or not it's costeffective, a few standees too. Place these up at-all the sites which may get you company. For instance, easily opened up a brand new DVD rental shop, I'd put these up at auditoriums, movies and outside university grounds. As a result, I am attracting the crowd that is most ideal for my company. Likewise, easily opened up a storage, I would put these up external restaurants and offices and at gas stations also. You'll be able to submit advertisements in magazines that fit in with the exact same niche as your organization after examining the fee-effectiveness.

Because so much of our information about organizations comes from the Web, I also suggest a web site. This can be a free resource also through such companies as Weebly and Google. Individuals buying a business in a particular place will likely undergo a searchengine (i.e. Google, Yahoo or AltaVista) and think of your site list classes available, schedules and price.

To The other hand, if you want individuals to believe that the interaction of your brand is actually made by real buyers, consider having a Blair Witch Project tactic. Get Yourself A camera and hit the streets. Furthermore, you can browse the mail you get and reproduce customers' feedback with total reliability (typos and all). If you were to think that "getting real" in your conversation will never work, verify the ratings for reality tvshows throughout the last decade. You will find loads of data supporting the truth that when people think it is the real-deal, success practices.

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