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# Niccolo Fontana Tartaglia

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Niccolo Fontana Tartaglia (1500-1557) was an Italian mathematician, an engineer (designing fortifications), surveyor (topography w/r best means of defense or offense), and bookkeeper. 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.

Tartaglia is perhaps best known today for his conflicts with Gerolamo Cardano. Cardano nagged Tartaglia into revealing his solution to some cubic equations, by promising not to publish them. Several years later, Cardano happened to see unpublished work by another mathematician who independently came up with the same solution as Tartaglia. As the unpublished work was dated before Tartaglia's, Cardano decided his promise could be broken, and included Tartaglia's solution in his next publication. In spite of the fact that Cardano credited his discovery, Tartaglia was extremely upset. He responded by publicly insulting Cardano personally as well as professionally.

Tartaglia is also known for giving an expression (Tartaglia's formula) for the volume of a tetrahedron (incl. any irregular tetrahedra) in terms of the distance values measured pairwise between its four corners:

$V = \sqrt{ \frac{1}{288} \begin{bmatrix}  0 & a^2 & b^2 & c^2 & 1 \\  a^2 & 0 & d^2 & e^2 & 1 \\ b^2 & c^2 & 0 & f^2 & 1 \\ d^2 & e^2 & f^2 & 0 & 1 \\  1 & 1 & 1 & 1 & 0  \end{bmatrix}. }$

This is in generalization of Heron's formula for the area of a triangle.

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