The ancient Greeks discovered them, but it wasn t until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty first century Along the way, he explains why irrational numbers are surprisingly difficult to define and why so many questions still surround them Fascinating and illuminating, this is a book for everyone who loves math and the history behind it....
|Title||:||The Irrationals: A Story of the Numbers You Can’t Count On|
|Number of Pages||:||165 Pages|
|File Size||:||594 KB|
|Status||:||Available For Download|
|Last checked||:||21 Minutes ago!|
The Irrationals: A Story of the Numbers You Can’t Count On Reviews
Other reviewers point out the amazing depth and breadth of Havil's mathematical journey, and they're right. But another wonderful facet: Havel's command of English, and his continual use of subtle metaphor is delightful, humorous and, frankly, shocking! This is an awesomely right/left brain balanced talent whose intellect is as much fun to watch as the proofs and historical adventure. "We hope with sufficient conviction for hand-waving to be a positive signal" he quips, as an example of his continual tongue in cheek about ponderous scientific method and epistemology. He is genius at making sure we don't take "axioms" too seriously, and what better secret and oyster pearl grain irritant is there than the irrationals? This isn't just subtle-- Havel often points out limits in many senses of the word, from the essence of defining irrationals to quotes like "It is terrifying to think how much research is needed to determine the truth of even the most unimportant fact" (Stendhal) and "One can measure the importance of a scientific work by the number of earlier publications rendered superflous by it" (Hilbert). (Wonder how this would apply to the succession of the planet's Prophets??).
I read this book on the recommendation of a mathematician friend after our many philosophical debates. I'm a physiker and cranky to boot. At the very edge of our understanding, there exists a mysterious set of constants. They have been increasingly observed in nature, socialized as precise with one additional decimal place as better instrumentation and computers will do. Then again, there is a problem ... these constants may not be numbers at all as we imagine numbers. At issue is plugging constants into formulas and performing algebraic manipulations to imagine that we might someday describe everything in an algorithm. I defer to Feynman to describe one of these constants, the fine structure constant that holds everything together ...
For mathematicians, teachers or just math lovers, very good. It can be read several times, each with a deeper
I had to read this book twice. The first time I skimmed it and shyed away from the proofs. That was a mistake. If one takes one's time and tries to get a gist of what the proofs are trying to show, the reader will get a glimpse into the mysteries of irrational numbers. I would recommend the readers have some familiarity with college level mathematics when approaching this book. The reader will come away from this book with a better understanding of how mathematicians struggled with the irrationals over history and expanded understanding of this pandora's box opened by the legendary Hippias who was a pythagorean who shared the secret of their existence to the world and as the legend goes was thrown overboard a ship by his angry brethren.You will learn about Greek geometric proofs of incommeasurables. Next you will be introduced to surd arithmetic in India and Islamic civilization,then Medieval Europeans then pick up the thread. The proofs of pi and e irrationality are worth a closer look and Algebraic and Trancendentals are discussed along with proofs of e and pi as transcendental numbers. The later chapters cover the 19th century rigorists in Germany as the hammer out definitions of the irrationals and the real numbers. The last chapter covers some of the applications of the study of irrationals.One chapter I really like has a good discussion of the randomness with regard to irrationals. If you willing to put in some effort an it is an illuminating book.