Traipse on Complex Numbers
Origin of Complex Numbers does present a challenge to anybody. Most of us are introduced to the complex numbers in our grade 8 when we learn to solve quadratic equation and we encounter sqrt(-ve number). I am currently taking complex analysis so I am fortunate to read some books and broswe through websites, so here is an easy way to understand these mysterious, imaginary numbers in a concrete way.
Historically five people whose name comes up have an interesting story. These people are Del Ferro,Fior,Tartaglia,Cardano, Ferrari and Bombelli.Del Ferro was the first person who is known to have come up with the solution of the cubic equation, since he didn't published much infact none of his publication has survived. The legend is he revealed his work to one of his pupil called Fior. However he revealed only one part of the solution. Not realizing this Fior become overconfident in his mathematical ability and met Tartaglia in a mathematical duel. Tartaglia solved all the 30 problems posed by Fior and established himself a force in mathematics from being a simple self taught teacher. History doesn't pain Tartaglia in a very good light. He is said to have not published his results so that he could won more mathematics competition. Then arrives Cardano a person who was an illegitimate, genius mathematician. Whose story is from rags to riches and then dying in ignomity. He was an Italian who tried several times to gain entry into influential mathematical circle but couldn't gain it until he proved his mettle by writing books and excelling in treating his patients. Once he arrived in the mathematical scence he was a force to reckon with. He persuaded Tartaglia to reveal his formula for cubic equation but Tartaglia entered into a secret pact with him not to reaveal it to other. Cardano had a terrific protege whose name was Ferrari and they discovered that its not Tartaglia who first discovered the formula for solving cubic equation but it was Del Ferro. So Del Ferro thought his promise to Tartaglia was not binding to him anymore and he published the result in his celebrated text Art magna. Tartaglia was infuriated and challenged him for mathematical duel. After much deleberations Tartaglia finally agreed to take on Ferrari, Cardano's protege. Much to his chagrin he finds him very much familiar with the nuances of mathematics and Tartaglia fleds the very same day. Thus Ferrari comes out of the shadow of Cardano. He goes on to find the general solution of fourh power equation and lived on a happy life unlike Cardano. Who suffers ignominity because of his son's act to poison his wife and his name in that conspiracy. His son is decapitated. The other son is equally incompetent and that tears apart Cardano. Finally comes Bombelli who after looking at the formula sees what all had previously overlooked and dismissed as unimportant and that is Bombelli's wild thought. I hope to keep updating this theory of complex number in my blog "Traipse on Mathematics" so keep watching that blog !!
Sumant
Historically five people whose name comes up have an interesting story. These people are Del Ferro,Fior,Tartaglia,Cardano, Ferrari and Bombelli.Del Ferro was the first person who is known to have come up with the solution of the cubic equation, since he didn't published much infact none of his publication has survived. The legend is he revealed his work to one of his pupil called Fior. However he revealed only one part of the solution. Not realizing this Fior become overconfident in his mathematical ability and met Tartaglia in a mathematical duel. Tartaglia solved all the 30 problems posed by Fior and established himself a force in mathematics from being a simple self taught teacher. History doesn't pain Tartaglia in a very good light. He is said to have not published his results so that he could won more mathematics competition. Then arrives Cardano a person who was an illegitimate, genius mathematician. Whose story is from rags to riches and then dying in ignomity. He was an Italian who tried several times to gain entry into influential mathematical circle but couldn't gain it until he proved his mettle by writing books and excelling in treating his patients. Once he arrived in the mathematical scence he was a force to reckon with. He persuaded Tartaglia to reveal his formula for cubic equation but Tartaglia entered into a secret pact with him not to reaveal it to other. Cardano had a terrific protege whose name was Ferrari and they discovered that its not Tartaglia who first discovered the formula for solving cubic equation but it was Del Ferro. So Del Ferro thought his promise to Tartaglia was not binding to him anymore and he published the result in his celebrated text Art magna. Tartaglia was infuriated and challenged him for mathematical duel. After much deleberations Tartaglia finally agreed to take on Ferrari, Cardano's protege. Much to his chagrin he finds him very much familiar with the nuances of mathematics and Tartaglia fleds the very same day. Thus Ferrari comes out of the shadow of Cardano. He goes on to find the general solution of fourh power equation and lived on a happy life unlike Cardano. Who suffers ignominity because of his son's act to poison his wife and his name in that conspiracy. His son is decapitated. The other son is equally incompetent and that tears apart Cardano. Finally comes Bombelli who after looking at the formula sees what all had previously overlooked and dismissed as unimportant and that is Bombelli's wild thought. I hope to keep updating this theory of complex number in my blog "Traipse on Mathematics" so keep watching that blog !!
Sumant
posted by Sumant at 1:18 AM
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