Eli Maor

Il pi greco lo conoscono tutti o quasi; ma non è il solo numero "molto interessante" per i matematici. Secondo a ben poca distanza c'è infatti il numero e, che vale circa 2,718 e appare anch'esso nei punti più diversi della matematica; dal calcolo dell'area sotto un'iperbole a quello degli interessi composti, dai logaritmi alle funzioni trigonometriche. Nella sua bella collana a basso prezzo che recupera varie opere di storia della matematica, la Princeton University Press ha recuperato show more questo testo dedicato per l'appunto a e. Il libro è scritto molto bene; richiede qualche competenza matematica ma risulta facilmente leggibile e interessante. La parte storica è molto completa che parte dalla nascita dei logaritmi, con divagazioni all'indietro verso Archimede e i problemi della quadratura, per arrivare alla scoperta della trascendenza del numero. I concetti vengono spiegati in maniera molto chiara, oserei dire meglio che quanto viene fatto a scuola da noi. Naturalmente ci sono anche divagazioni su altri numeri famosi, π e i prima di tutti; d'altra parte tutti questi numeri sono (stranamente?) correlati tra loro... show less

I doubt this book appeals to readers with 'modest background in mathematics' as the cover promises. 'e' is the base of the natural logarithm. I vaguely recalled that e was the only number that was its own derivative. This book is at its best describing the discovery of 'e', and its historical import.

As a non-mathematician I had to skip the most complicated moments, but still appreciated the overall story.

I majored in physics in college, where I learned about overtones and their connection to musical tuning. So I didn't learn much from this book! But if this is not familiar territory for you, it's a nice introduction. It's an easy read... well, I guess there is a bit a math sprinkled in, which might frighten off some readers. But the formulas are not essential to understanding the story.

My own fascination is with alternate tunings and the history and diversity of tuning. This book was show more disappointing in that regard. Maor talks about how keys might have emotional color... but he can't step out of equal temperament to do it! Equal temperament was not in use in the 18th Century! Of course in a quick read like this, it's not possible for the author to dive in very deeply! He mentions that tuning has a history, but, ah! A paragraph or two could have opened the door!

The book culminates with a sketch of the parallel lives of Schoenberg and Einstein. What might relativistic music look like? Yeah, I have thought so much about this stuff... a book like this is just a series of missed opportunities! But again, for somebody just dipping their toes in the water... Still... ha, I got to do a junior year research paper with Robert Dicke, a top general relativity professor. A curious feature of general relativity... there are inertial frames of reference that are distinct from accelerating frames. Why are inertial frames inertial? What is the physical cause that results in some frames being inertial while others are accelerating?

So I will relate that to tonal music. I create lots of music that is not at all tonal in that it doesn't follow any rules about dominant vs tonic etc. But it is strongly tonal in that it all about long range order and consonance. There are pitch classes that occur more often, that form a base, a sort of frame of reference. Anyway, the Maor writes about it, it seems like we are stuck between extreme choices, conventionality and nonsense. No! There is a vast universe of possibilities! Yeah, just because unification of quantum mechanics and general relativity through String Theory was a bust, that doesn't mean that some other mathematically beautiful approach might not work! show less

When I was a single digit prime number, I bought a ten cent comic book that was different from all the rest. It was called Donald Duck in Mathematics Land, and it was all about the absolute magic of numbers in geometry. It was a treasure and I still have it, carefully pressed flat and kept from the ravages of light.

Now just 50 years later, come a couple of number theory heavyweights, one in math and one in math-based art, one-upping Donald. Beautiful Geometry makes art of science and sense show more of math.

The science dates back to the golden age of Greece, that less-than-hundred year period where the Greeks ruled the intellectual world, spent their time racking up truckloads of discoveries, and elevating science to unheard of heights. Interestingly, there were no generalizations in the approach of the Greeks. Each time they discovered a variation or new instance, it became a new theorem, even though it might describe the same phenomenon as another theorem. Nothing was insignificant in the golden age. And though they did not have a real number system to work with (that had to wait till 1200 AD), and a lot of what they proposed was (ultimately) incorrect, they made remarkable contributions and remarkable progress.

There are 51 three page chapters, each illustrating magic of some sort in numbers and their geometric origin and/or display. The middle page of each chapter is a full page color work of art employing the topic of the chapter.

For those not mathematically inclined, it will be work to understand it all. But it is written as simply and basically as mathematics can be, and the overall effect is one of childlike fascination with the magic of it all. From equivalence to symmetry to infinity, it’s all here, updating and collecting facets of number theory that have occupied and obsessed the minds of mathematicians and philosophers for more than 2000 years. show less