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A review by brettt
An Imaginary Tale: The Story of the Square Root of Minus One by Paul J. Nahin
2.0
Of all the people who probably hide their heads at the goofs they have made, the person who named "imaginary" numbers is probably among them as far as the field of mathematics is concerned.
So-called "imaginary" numbers describe the square roots of negative numbers, which are impossible to calculate using plain integers. The square root of 1, for example, is 1 because 1x1=1. But the square root of -1 seems impossible to figure, because the only way to get to -1 is to multiply two different numbers together. A negative number multiplied by another negative number leaves a positive number, not a negative one. At some point, mathematicians decided that there would be a square root of -1, and it would just be a 1 that was on another "axis" than the regular positive-negative line. But since the number didn't seem to have any real-world analogue like positive and negative numbers did, it somehow got hung with the tag, "imaginary." So today we say that the square root of negative 1 is i. The square root of -4 is 2i, and so on.
Retired electrical engineering professor Paul Nahin outlines some of the development of i through the history of mathematics in An Imaginary Tale. Some early cultures refused to acknowledge the existence of a quantity that could be squared to form a negative number, and even into the Renaissance and enlightenment years the so-called "imaginary" numbers were considered at best unimportant. They were not useful except in specialized cases and it seemed even mathematicians had reservations about dealing with numbers that didn't represent any real quantity.
Today, i and its counterparts find widespread use in many areas of math, and the only reservations that seem to continue deal mostly with the use of the word "imaginary." Nahin explores how important i is in many fields of engineering, especially his own. This part of the book -- about the latter two-thirds -- is heavily laden with equations and formulas and is going to be beyond most non-mathematician or non-engineer readers. He probably would have had to lengthen the book considerably to bring that subject matter within the grasp of the lay reader, but that doesn't make the string of equations and engineering language any easier to navigate.
Original available here.
So-called "imaginary" numbers describe the square roots of negative numbers, which are impossible to calculate using plain integers. The square root of 1, for example, is 1 because 1x1=1. But the square root of -1 seems impossible to figure, because the only way to get to -1 is to multiply two different numbers together. A negative number multiplied by another negative number leaves a positive number, not a negative one. At some point, mathematicians decided that there would be a square root of -1, and it would just be a 1 that was on another "axis" than the regular positive-negative line. But since the number didn't seem to have any real-world analogue like positive and negative numbers did, it somehow got hung with the tag, "imaginary." So today we say that the square root of negative 1 is i. The square root of -4 is 2i, and so on.
Retired electrical engineering professor Paul Nahin outlines some of the development of i through the history of mathematics in An Imaginary Tale. Some early cultures refused to acknowledge the existence of a quantity that could be squared to form a negative number, and even into the Renaissance and enlightenment years the so-called "imaginary" numbers were considered at best unimportant. They were not useful except in specialized cases and it seemed even mathematicians had reservations about dealing with numbers that didn't represent any real quantity.
Today, i and its counterparts find widespread use in many areas of math, and the only reservations that seem to continue deal mostly with the use of the word "imaginary." Nahin explores how important i is in many fields of engineering, especially his own. This part of the book -- about the latter two-thirds -- is heavily laden with equations and formulas and is going to be beyond most non-mathematician or non-engineer readers. He probably would have had to lengthen the book considerably to bring that subject matter within the grasp of the lay reader, but that doesn't make the string of equations and engineering language any easier to navigate.
Original available here.