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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.
Some images inside the book are unavailable due to digital copyright restrictions.
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Opisan je evolucijski pomen mejoze in vzroki za prevlado spolnega načina razmnoževanja pri višjih rastlinah ter pomen prerazporejanja genov (rekombinacija) v profazi prve zoritvene delitve. ...Predstavljen je razvoj mejoze iz mitoze in razlike med tema celičnima delitvama. Opisano je nabiranje cvetnih brstov čemaža za pripravo mejotskih preparatov. Cvetne brste čemaža smo nabirali v marcu in aprilu 2008. Največ mejotskih faz smo opazili pri cvetnih brstih nabranih v tretjem tednu v mesecu marcu. Optimalna dolžina cvetnih brstov je bila 1 do 1,5 cm. V aprilu so bili cvetni brsti preveč razviti, lahko smo opazovali le pelodna zrna.
Število rojstev v Sloveniji se je v dobrih dvajsetih letih skoraj prepolovilo, priseljevanje se je ustavilo, povečuje se število starejših prebivalcev, medtem ko skupno število prebivalcev celo ...nazaduje. Za ta pojav smo uporabljali izraz staranje prebivalstva, ki pa je nepravilen. Pomeni namreč, da je vedno več starejših prebivalcev, ker dočakajo višjo starost, to pa je vendar zelo dobro. Velika nerodnost je torej prav v izrazu staranje prebivalstva, s katerim v resnici hočemo izpostaviti problem zniževanja števila rojstev, ne pa kot problem označevati vedno kasnejše umiranje ljudi. Stanje, ko je v enem letu število umrlih enako številu rojenih, imenujemo prebivalstveni prag. Tovrstna problematika v Sloveniji se je zelo zaostrila, ker je naša država že pod prebivalstvenim pragom, ne pa zaradi staranja prebivalstva. Nazadovanje skupnega števila prebivalcev, močno znižanje števila mladih in na drugi strani večanje števila starih prebivalcev zahtevajo tudi nove pristope k planiranju, ki ne more več temeljiti na neki imaginarni rasti, ampak na kakovosti razvoja. To velja tudi za mesta.
Provider: - Institution: - Data provided by Europeana Collections- Papir s številko 10, ki je bil obešen v učilnici prvega razreda na POŠ Ribno.- All metadata published by Europeana are available ...free of restriction under the Creative Commons CC0 1.0 Universal Public Domain Dedication. However, Europeana requests that you actively acknowledge and give attribution to all metadata sources including Europeana
