Rafael Bombelli 1526-1572.

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Presentation transcript:

Rafael Bombelli 1526-1572

Life and Times Bombelli was mentored by Pier Francesco Clementi- an Engineer-Architect Lived in Bologna, Italy as an hydraulic engineer draining wetlands for the Apostolic Camera (Catholic Church) Followed works done by del Ferro, Cardan, Ferrari and Tartaglia The papal states Pope Paul III (1534-1549) The Spanish Inquisition was founded in 1478- The Church was still VERY powerful in Bombelli’s time. His work was done after Copernicus but before Galileo.

Square Roots Bombelli’s method using continued fractions to calculate square roots: If the + sign is used, a2 = the square below n, If the – sign is used, a2 = the square above n.

An Example:

First wrote down how to calculate with negative numbers First wrote down rules of how to multiply, add and subtract imaginary numbers 3 Books (“Geometrical Parts”4&5 never completed) Book III included 143 problems from Diophantus’ Arithmetica 143 out of 272 problems in the book. He worked on a translation of Diophantus’ Arithemetica with Antonio Maria Pazzi

Rules of Negative Numbers Plus times plus makes plus Minus times minus makes plus Plus times minus makes minus Minus times plus makes minus Plus 8 times plus 8 makes plus 64 Minus 5 times minus 6 makes plus 30 Minus 4 times plus 5 makes minus 20 Plus 5 times minus 4 makes minus 20

Rules of Complex Numbers Plus of minus times plus of minus makes minus (+√-n )(+√-n) = -n Plus of minus times minus of minus makes plus (+√-n )(-√-n) = +n Minus of minus times plus of minus makes plus (-√-n)(+√-n) = +n Minus of minus times minus of minus makes minus (-√-n)(-√-n) = -n

Bombelli’s Notation Roots-Quadrato(2), cubo(3),quadroquadrato(4), numero detto primo relato(5)

Thank You!! References J J O'Connor and E F Robertson, “Rafael Bombelli” July 16, 2006 http://www-history.mcs.st-andrews.ac.uk/Biographies/Bombelli.html A very detailed biography Curtin, Sandifer, Stoudt, “Rafael Bombelli’s L’Algebra” July 16, 2006 http://nsm1.nsm.iup.edu/gsstoudt/history/bombelli/bombelli.pdf An interesting site discussing L’Algebra Wikipedia, “Rafael Bombelli” July 16,2006 http://en.wikipedia.org/wiki/Rafael_Bombelli A short biography with description of his method to calculate square roots Kevin Wood © August 2006