Today complex numbers have such widespread practical use--from
electrical engineering to aeronautics--that few people would expect the
story behind their derivation to be filled with adventure and enigma. In
An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one
of mathematics' most elusive numbers, the square root of minus one, also
known as i. He recreates the baffling mathematical problems that
conjured it up, and the colorful characters who tried to solve them.
In 1878, when two brothers stole a mathematical papyrus from the ancient
Egyptian burial site in the Valley of Kings, they led scholars to the
earliest known occurrence of the square root of a negative number. The
papyrus offered a specific numerical example of how to calculate the
volume of a truncated square pyramid, which implied the need for i. In
the first century, the mathematician-engineer Heron of Alexandria
encountered I in a separate project, but fudged the arithmetic;
medieval mathematicians stumbled upon the concept while grappling with
the meaning of negative numbers, but dismissed their square roots as
nonsense. By the time of Descartes, a theoretical use for these elusive
square roots--now called "imaginary numbers"--was suspected, but efforts
to solve them led to intense, bitter debates. The notorious i finally
won acceptance and was put to use in complex analysis and theoretical
physics in Napoleonic times.
Addressing readers with both a general and scholarly interest in
mathematics, Nahin weaves into this narrative entertaining historical
facts and mathematical discussions, including the application of complex
numbers and functions to important problems, such as Kepler's laws of
planetary motion and ac electrical circuits. This book can be read as an
engaging history, almost a biography, of one of the most evasive and
pervasive "numbers" in all of mathematics.
