Rafael Bombelli
Encyclopedia : R : RA : RAF : Rafael Bombelli
Rafael Bombelli (1526–1573) was an Italian mathematician.
Born in Bologna, he is the author of a treatise on algebra and is a central figure in the understanding of imaginary numbers.
Bombelli used a method related to continued fractions to calculate square roots. His method for finding [ \sqrt ] sets [ n=(a\pm r)^2=a^2\pm 2ar+r^2\ ] with [ 0
He was the one who finally managed to settle the problem with imaginary numbers. In Algebra 1569, Bombelli solved equations, using the method of del Ferro/Tartaglia, he introduced +i and -i and described how they both worked in Algebra.
The lunar crater Bombelli is named after him.
From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.]. Repeated substitution of the expression on the right hand side for [r] into itself yields a continued fraction >
\frac >
\frac >
\cdots ]
for the root but Bombelli is more concerned with better approximations for [r]. The value chosen for [a] is either of the whole numbers whose squares [n] lies between. The method gives the following convergents for [\sqrt\ ] while the actual value is 3.605551275... :
The last convergent equals 3.605550883... . Bombelli's method should be compared with formulas and results used by Hero and Archimedes. The result [\frac<\sqrt<\frac] used by Archimedes in his determination of the value of [\pi \ ] can be found by using 1 and 0 for the initial values of [r].External link
References
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.