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Sto caricando le informazioni... How Mathematics Happened: The First 50,000 Yearsdi Peter Strom Rudman
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Iscriviti per consentire a LibraryThing di scoprire se ti piacerà questo libro. Attualmente non vi sono conversazioni su questo libro. I have been looking for a book about the early history of mathematics for some time - and this fit the bill. Without upper level math such as group theory, I can't understand the history of math much after the calculus was invented, so this book is just right. This book does a very good job of describing the early history of counting, numerical systems, early addition, subtraction, multiplication and division. Rudman does a good job of explaining current methods of calculation and then takes you back to the Egyptians, Babylonians and Greeks. Without taking the time to work out all the problems given, I was able to understand most of the methods presented. Rudman is also very clear about where he is conjecturing, which of his ideas are supported by archaeological evidence, and which ideas are generally accepted by scholars of early mathematics. nessuna recensione | aggiungi una recensione
In this fascinating discussion of ancient mathematics, author Peter Rudman does not just chronicle the archeological record of what mathematics was done; he digs deeper into the more important question of why it was done in a particular way. Why did the Egyptians use a bizarre method of expressing fractions? Why did the Babylonians use an awkward number system based on multiples of 60? Rudman answers such intriguing questions, arguing that some mathematical thinking is universal and timeless. The similarity of the Babylonian and Mayan number systems, two cultures widely separated in time and space, illustrates the argument. He then traces the evolution of number systems from finger counting in hunter-gatherer cultures to pebble counting in herder-farmer cultures of the Nile and Tigris-Euphrates valleys, which defined the number systems that continued to be used even after the invention of writing. With separate chapters devoted to the remarkable Egyptian and Babylonian mathematics of the era from about 3500 to 2000 BCE, when all of the basic arithmetic operations and even quadratic algebra became doable, Rudman concludes his interpretation of the archeological record. Since some of the mathematics formerly credited to the Greeks is now known to be a prior Babylonian invention, Rudman adds a chapter that discusses the math used by Pythagoras, Eratosthenes, and Hippasus, which has Babylonian roots, illustrating the watershed difference in abstraction and rigor that the Greeks introduced. He also suggests that we might improve present-day teaching by taking note of how the Greeks taught math. Complete with sidebars offering recreational math brainteasers, this engrossing discussion of the evolution of mathematics will appeal to both scholars and lay readers with an interest in mathematics and its history. Non sono state trovate descrizioni di biblioteche |
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Google Books — Sto caricando le informazioni... GeneriSistema Decimale Melvil (DDC)510.93Natural sciences and mathematics Mathematics General Mathematics Biography And History Ancient WorldClassificazione LCVotoMedia:
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It tells the (pre)(hi)story of mathematics from the days of Neolithic hunter-gatherers to the timeof the famous ancient Greek mathematicians, such as Pythagoras. This means working with very limited data and there are a lot of assumptions, suppositions and intuitions filling in the gaps between the data. Of course that is the nature of all archaeology, which is, after all, the task of reconstructing a culture from a subset of its material productions. Rudman is very good in this territory; he is very clear about what is a fact, what is a hypothesis, what is a theory, what the assumptions are, what is his personal view and what is generally accepted theory.
For me, the book got more interesting as it went along, largely because the maths itself got more interesting; at the outset there is only counting, by the end there is rigorous proof of the irrationality of root 2 and the Pythagoras Theorem (which it turns out was known but not proven well before Pythagoras came on the scene).
I do think the book has flaws, though. There are plenty of "fun questions" through out - but for me most of them weren't fun. Fortunately they are easily ignored. Rudman also "pulls a Dawkins" with several snide remarks about religion and theists that have no place in the book at all and the final chapter on maths teaching methods has some obviously fallacious arguments mixed in with sensible observations - but that chapter is just as out of place in this book as comments about the "intellectual weakness" of theists. Rudman's terminology seems a little obfuscatory on occassions, too: what's a frustrum? What's a truncated pyramid? I bet you can guess what the latter is - but a frustum is the same thing! He also uses "prism" when he means cuboid. That said, the arguments are generally clear.
Overall I feel that an intriguing topic has been poorly but not hopelessly served by this book - a better writer could have improved it greatly. ( )