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 colourful 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.
發表於2025-01-10
An Imaginary Tale: The Story of "i" [the square root of minus one] 2025 pdf epub mobi 電子書 下載
僅以此文紀念中學時候讀過的數學名著通俗譯叢 記得第一次接觸這套書,是在初中的時候,有次上海書城未開業前的內部開放,我跟著一群原來住在那裏的居民混瞭進去,就看到瞭這套書的前三冊:數論妙趣,新的黃金時代和數學娛樂問題,還依稀記得當時嗜書(特彆是好的數學書)如命...
評分僅以此文紀念中學時候讀過的數學名著通俗譯叢 記得第一次接觸這套書,是在初中的時候,有次上海書城未開業前的內部開放,我跟著一群原來住在那裏的居民混瞭進去,就看到瞭這套書的前三冊:數論妙趣,新的黃金時代和數學娛樂問題,還依稀記得當時嗜書(特彆是好的數學書)如命...
評分二次方程 1)古希臘數學傢丟番圖,為求解某個幾何問題,建立一元二次方程,求解過程中遇到負數開平方(虛數)。他認為該解無意義,方程對應的幾何問題不存在實際答案。 2)後來,印度數學傢也遇到類似的問題,與丟番圖持同樣觀點。 三次方程 3)後來,意大利一個叫費羅的數學傢...
評分二次方程 1)古希臘數學傢丟番圖,為求解某個幾何問題,建立一元二次方程,求解過程中遇到負數開平方(虛數)。他認為該解無意義,方程對應的幾何問題不存在實際答案。 2)後來,印度數學傢也遇到類似的問題,與丟番圖持同樣觀點。 三次方程 3)後來,意大利一個叫費羅的數學傢...
評分二次方程 1)古希臘數學傢丟番圖,為求解某個幾何問題,建立一元二次方程,求解過程中遇到負數開平方(虛數)。他認為該解無意義,方程對應的幾何問題不存在實際答案。 2)後來,印度數學傢也遇到類似的問題,與丟番圖持同樣觀點。 三次方程 3)後來,意大利一個叫費羅的數學傢...
圖書標籤: 科普 數學 英文原版 數學 教材 Mathematics
An Imaginary Tale: The Story of "i" [the square root of minus one] 2025 pdf epub mobi 電子書 下載