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The Golden Ratio by Mario Livio. Anybody read it?Me and my sister were at a mall in New Jersey when we wandered into a boxstore. I quickly made my way to the science section to see if they had any good math or science books. I picked up a book called "The Golden Ratio." not knowing what it was. But below the title it said "the story of Phi" now I'm not sure who this mario livio is, but anyone who would write an entire book about a single number, is definitly the kind of author who's work I'd like to read! Last edited by mikau (20060619 02:47:34) A logarithm is just a misspelled algorithm. #2 20060619 02:39:21
Re: The Golden Ratio by Mario Livio. Anybody read it?Copied from the front and back flap: Last edited by mikau (20060619 02:42:57) A logarithm is just a misspelled algorithm. #3 20060619 03:01:54
Re: The Golden Ratio by Mario Livio. Anybody read it?a formula for phi is also sqrt(5)/2 + 0.5, and im not sure if it says it in the book or not, it probably does Last edited by lucadeltodesco (20060619 03:12:52) The Beginning Of All Things To End. The End Of All Things To Come. #4 20060619 04:10:48
Re: The Golden Ratio by Mario Livio. Anybody read it?yeah I calculated that with the quadratic formula ( sqrt (5) + 1 )/ 2 but the fibonacci formula I'd never seen before! Remarkable! A logarithm is just a misspelled algorithm. #5 20060619 04:20:39
Re: The Golden Ratio by Mario Livio. Anybody read it?i still find the most remarkable thing about phi The Beginning Of All Things To End. The End Of All Things To Come. #6 20060619 07:35:52
Re: The Golden Ratio by Mario Livio. Anybody read it?cool, those appear to be rearranged forms of the equation (phi + 1)/phi = phi, which is the equation you get from the line segment definition. A logarithm is just a misspelled algorithm. #7 20060619 09:23:05
Re: The Golden Ratio by Mario Livio. Anybody read it?Don't mess with that number! It is the Devil's constant! #8 20060619 13:58:08
Re: The Golden Ratio by Mario Livio. Anybody read it?hehehe! Creepy! A logarithm is just a misspelled algorithm. #9 20060619 14:21:53
Re: The Golden Ratio by Mario Livio. Anybody read it?This post has inspired me to work out some expressions for φ. Being a fan of infinite series representations of special constants, I chose to focus on that area: In the process of deriving the third equation above, I came across a noteworthy sum: I'll spend some more time finding expressions for φ and other constants later. Edit: For some reason I had put the negative in formula two outside of the first sum. Interestingly enough, this made it an expression for 1/φ. Last edited by Zhylliolom (20060619 22:08:09) #10 20060619 17:01:44
Re: The Golden Ratio by Mario Livio. Anybody read it?I suppose the "noteworthy sum" for i can be used to simplify the third expression. I don't know why I didn't notice this before. Perhaps I liked the more complex formula and didn't want to change it. Anyway: On second thought, this formula is more beautiful due to the compactness compared to its other form. Also, I prefer the relation of φ with constants not including itself, at least in this case. On the topic of the book, I have not read it. I am becoming more interested in φ though, and I see this book everytime I go to buy more math textbooks, so perhaps I will give in a purchase it in the future. Edit: A period was not where it needed to be. I can't handle mistakes like those! Last edited by Zhylliolom (20060619 17:03:22) #11 20060619 19:33:55
Re: The Golden Ratio by Mario Livio. Anybody read it?Impressive sums Zhylliolom. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #12 20060620 01:09:33
Re: The Golden Ratio by Mario Livio. Anybody read it?is i ever usefull? A logarithm is just a misspelled algorithm. #13 20060620 01:11:06
Re: The Golden Ratio by Mario Livio. Anybody read it?
no it isnt The Beginning Of All Things To End. The End Of All Things To Come. #14 20060620 01:38:30
Re: The Golden Ratio by Mario Livio. Anybody read it?Did you do that in degrees or radians? I get 1.618... and my calculator even gives me: "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #15 20060620 01:48:45
Re: The Golden Ratio by Mario Livio. Anybody read it?
Sure it is. Actually, I was just reading about this today. I was thinking of starting a new topic, but I'll just post it here. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #16 20060620 06:31:51
Re: The Golden Ratio by Mario Livio. Anybody read it?interesting, but that is not what I meant by usefull. Could 'i' ever be used to solve a real world problem? (in a formula to produce a real number solution) for instance, adding i to both sides or multiplying both sides by i allowing you to rearranging it into another form that eventuallly eliminates i giving you a real number solution? A logarithm is just a misspelled algorithm. #17 20060620 06:48:05
Re: The Golden Ratio by Mario Livio. Anybody read it?I guess my first question to you would be, who cares about the real world? "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #18 20060620 07:40:15
Re: The Golden Ratio by Mario Livio. Anybody read it?
... but not yet ... "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #19 20060620 08:18:49
Re: The Golden Ratio by Mario Livio. Anybody read it?Sure. I didn't really take my time on that post, more or less just ran through it. There is a lot more detail, but most of it involves groups and fields, which are hard to explain in a page or two. I'll see if I can come up with an easy way to explain those. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #20 20060620 11:17:45
Re: The Golden Ratio by Mario Livio. Anybody read it?"I guess my first question to you would be, who cares about the real world?" A logarithm is just a misspelled algorithm. #21 20060620 11:28:03
Re: The Golden Ratio by Mario Livio. Anybody read it?
i has many applications outside of pure mathematics. In special relativity, time is treated as imaginary in Minkowski space in order to make it symmetric to space: the fourth dimension, time, is given as x_{4} = ict. Quantum mechanics is littered with imaginary numbers. The example of i from quantum mechanics which springs to my mind instantly is Schrödinger's equation: I know imaginary numbers play a role in electrical engineering as well, but sadly I do not have as much experience as I wish to in that area. #22 20060620 11:31:11
Re: The Golden Ratio by Mario Livio. Anybody read it?Until I can play a game where every object is made up of atoms which act exactly as atoms in the real world, I will always want more. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #23 20060620 11:41:21
Re: The Golden Ratio by Mario Livio. Anybody read it?agreed! A logarithm is just a misspelled algorithm. #24 20060621 01:31:55
Re: The Golden Ratio by Mario Livio. Anybody read it?even then, i would prefer to have all those atoms also made of the sub atomic particles, all acting as they would in real life Last edited by lucadeltodesco (20060621 01:33:10) The Beginning Of All Things To End. The End Of All Things To Come. #25 20060621 07:34:35
Re: The Golden Ratio by Mario Livio. Anybody read it?And we could all be simulations in that very computer, and not even know it! "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman 