Rafael Bombelli
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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 
sets 
with 
from which it can be shown that 
. Repeated substitution of the expression on the right hand side for r into itself yields a continued fraction
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 
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 
used by Archimedes in his determination of the value of 
can be found by using 1 and 0 for the initial values of r.
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.
[edit] External link
- Template:MacTutor Biofasf
[edit] References
- Morris Kline, Mathematical Thought from Ancient to Modern Times, 1972, Oxford University Press, New York, ISBN 0-19-501496-0
- David Eugene Smith, A Source Book in Mathematics, 1959, Dover Publications, New York, ISBN 0-486-64690-4
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