The Golden Ratio

raceBannon writes "The book surprised and fascinated me. I thought it was going to be solely about the Golden Ratio. Mario Livio does cover the topic but along the way he throws in some mathematical history and even touches on the idea that math may not be a universal concept spread across the galaxy." Read on for the rest of raceBannon's review.

The Golden Ratio
author	Mario Livio
pages	320
publisher	Broadway
rating	7/10
reviewer	raceBannon
ISBN	0767908155
summary	Through telling the tale of the Golden Ratio, Livio explains how this simple ratio pops up in all kinds of physical phenomenon and debunks the idea that the ratio is present in many famous man-made structures and art work. Along the way, he provides historical tidbits regarding some of the well-known and not so well-known mathematicians throughout the ages and he tells the story of some of the more famous and not so famous mathematical advances. Finally, he discusses the possibility that mathematics may represent some kind of global truth that exists throughout the cosmos.

I have to admit that it is a little spooky to me that this ratio, this irrational number (1.6180339887...), pops up in many varied natural phenomena from how sunflowers grow to the formation of spiral galaxies; not to mention that the Golden Ratio and the Fibonacci Series are related. It makes you want to think that there is a God with a plan.

The Golden Ratio is defined as follows: In a line segment ABC, if the ratio of the length AB to BC is the same as the ratio of AC to AB, then the line has been cut in extreme and mean ratio, or in a Golden Ratio called Phi.

On the flip side, Livio squarely debunks the idea that the Golden Ratio is present in many famous paintings and architecture that has been postulated in previous books. He rightly points out that you can find the Golden Ratio in anything depending on where you decide to place the measuring tape. The idea that the Golden Ratio is such a symbol of universal beauty that it appears by accident in our great man-made buildings and artwork does not carry any weight. I think Livio makes his point.

He also uses the Golden Ratio as a framework to illuminate other historical tidbits about key mathematical figures, guys like Pythagoras and Euclid, who continue to affect the mathematical world to this day. I love this kind of stuff; the historical context of how and why these legends did what they did is very interesting to me. For example, I did not know that Euclid himself did not discover geometry or even make any great new contributions to the field in terms of ways to apply it. What he is famous for is organizing the information into a coherent fashion. He was a teacher of the highest order; so much so that Abraham Lincoln himself used Euclid's texts, unchanged after all those years, to learn the subject back in Lincoln's log cabin days.

The book is not all a philosophical discussion. Livio does use some simple math examples to make his points but it was at a level that I could follow. According to my college professor, I escaped College Calculus by sheer luck. Livio does provide the rigorous math examples in appendices at the end of the book (I did not bother with these).

Finally, Livio takes a shot at the idea that mathematics is a universal concept across the entire universe. To be honest, I have always assumed that it was. After all, I am a Trekkie and this concept goes unstated throughout all four TV series. The idea that mathematics is a human construction and probably holds no water in another civilization that grew up on the other side of the universe makes a lot of sense to me. I have to admit; I need to ponder that one for a while.

I recommend this book. If you like the history of science, your high school algebra class is just a little more than a dark fog in your memory, and you get a charge out of scientific mysteries, you will not be disappointed.

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It works, sorta..

[grub]

Out of every 1000 slashdotters, 1.6180339887... will have had sex with a real woman.

The Galaxy??

[Gorimek]

The concept of math isn't even spread very far on this planet.

The Golden Ratio

[Anonymous Coward]

He who has the gold, makes the ratio.

Sounds like an interesting book

[Anonymous Coward]

With a title like that I was expecting 320 pages of this:

1.6180339887498948482045868343656381177203091798 05 76286213544862270526046281890244970720720418939113 74847540880753868917521266338622235369317931800607 66726354433389086595939582905638322661319928290267 88067520876689250171169620703222104321626954862629 63136144381497587012203408058879544547492461856953 64864449241044320771344947049565846788509874339442 21254487706647809158846074998871240076521705751797 88341662562494075890697040002812104276217711177780 53153171410117046665991466979873176135600670874807 10131795236894275219484353056783002287856997829778 34784587822891109762500302696156170025046433824377 64861028383126833037242926752631165339247316711121 15881863851331620384005222165791286675294654906811 31715993432359734949850904094762132229810172610705 96116456299098162905552085247903524060201727997471 75342777592778625619432082750513121815628551222480 93947123414517022373580577278616008688382952304592 64787801788992199027077690389532196819861514378031 49974110692608867429622675756052317277752035361393 ...

Opinion, Mr. Spock?

[ackthpt]

"Captain, I believe there is a 1.6180339887 percent probability that any security officers beamed down to the planet will survive."

Re:Movie

[ath0mic]

...which I think also holds the record for the "longest movie title in history."

:)

Re: Da Shitty Code

[Anonymous Coward]

Dan Brown is the greatest writer of all time.

Provided we ignore EVERY OTHER WRITER EVER.

Re:Mathematics not universal?

[kfg]

I offer this argument to those who state "You create your own reality."

I kick them in the shin.

Then say, "Why did you do that?"

KFG

Intelligent marketting strategy for stupid ideas

[dtfinch]

He probably just caught on to the idea that if you say something outrageous enough in your books, like math is wrong, people will buy them.

Phi

[Rupert]

I hate it when people use extreme amounts of decimal precision when talking about irrational numbers. Really, is 1.6180339887 (or 1.6180339887498948482045868343656) much more informative than 1.618? If you're going to do calculations with it, use the exact value:

1/2 * (sqrt(5) + 1)

and sort out the irrational bits at the end, rather than introduce rounding errors at the beginning.

That's just a rationalisation, of course. My real reason for complaining about decimals is that it feels wrong. 1.6180339887 does not look like a profound number. It's like the number is a beautiful woman, and the decimal representation is the pornographic pictures she posed for when she was young and needed the money. Yes, it looks like her, and it may even be useful. But the real thing is *so* much better.

Re:A god with a plan?

[Geckoman]

What would be evidence of a creator would be if things did NOT follow what was natural and obvious. If these things did NOT follow the golden ratio and other straight math.. if we could find no explanation for why things had a weird ratio, or weird behavior.. no explanation from the current or possible past enviroment to explain how something evolved.... come to me with that, then we can talk about a creator.

If God had intentionally inserted all these frequently recurring constants and ratios everywhere, then they, like the Babelfish, would be proof of God's existence. That would defy faith, and He would disappear in a poof of logic.

Then, unfortunately, I'm afraid we'd all get hit by a bus....

Re:Numbers are numbers

[Anonymous Coward]

Aliens could call them Borgolsmocks in their base-182, but the fact still remains that a Borgolsmock cannot be divided evenly

Please define the following in absolute, universal terms:

cannot:
be:
divide:
evenly:

Re:Numbers are numbers

[Lemmeoutada Collecti]

Borgolsmock is divisible using a thersian constant. To assume that just because your single dimensional mathematics cannot divide a borgolsmock does not similarly limit n-dimensional. Why the mere act of division is a limitation of linearly conecived time, a limitation we have never faced.

Aside from which, where you see a single item, I percieve an infinite semi recursive series. There are more than one apple in that one apple. There are an infinite (using your limited numbering) number of apples. That apple you call 'one' in fact contains the entirety of it's temporal measurement, which is a bounded infinite series. So now tell me about this concept you call singularity?

Re:math is not universal?

[Timmeh]

HEY! Don't push your modernist science bullshit on me, PATRIARCH. My goddess awakening mentor told me about you so-called intellectuals. Using 'symbols' and 'information' is just another form of OPPRESSION.

To which the sage answer

[Sunnan]

"Do what?"

Interesting...

[cr0sh]

My wife just gave me this book a couple of days ago as a "surprise" present. I suppose it was after I noted how fascinating the ratio was, and how it appears in nature, among other areas. I also surmised that I could attempt to embody the ratio in some manner into a bookcase we will be building (I realize I could never make it exact, but I probably could get it within a few decimal places in some manner).

I am lucky - I am a geek with a geeky wife - go figure...

Re:Numbers are numbers

[Wind_Walker]

And maybe if you inverted the warp plasma through the deflector dish, you could create an inverse tachyon field that could disrupt that thersian constant! Make it so, Number One!

You see, I was limiting myself to thinking of... what's the word... reality. I was talking about plausable scenarios of intelligent extra-terrestrial life. You've obviously spent too much time reading Sci-Fi novels and not enough time in what we like to call the "real world" - and it's not that shitty MTV show you watch.

Re:Mathematics not universal?

[KurtP]

I answer: "Clearly, I am a masochist."

Now it all makes sense.

[Talinom]

The idea that mathematics is a human construction and probably holds no water in another civilization that grew up on the other side of the universe makes a lot of sense to me.

So that is why all of those UFOs are crashing all over the place.

Re:To which the sage answer

[criordan]

And they respond by kicking you in the shin again.

The Golden Ratio

[t0ny]

The Golden Ratio- He who has the gold makes the ratio.

Or something like that...

It think the golden ratio is something like this..

[Anonymous Coward]

I think it's something like where 1/(1+x) = x (or if you like) x^2 + x = 1 (or roughly)
0.61803398874989484820458683436563811772 0309179805 76286213544862270526046281890244970720720418939113 74847540880753868917521266338622235369317931800607 66726354433389086595939582905638322661319928290267 88067520876689250171169620703222104321626954862629 63136144381497587012203408058879544547492461856953 64864449241044320771344947049565846788509874339442 21254487706647809158846074998871240076521705751797 88341662562494075890697040002812104276217711177780 53153171410117046665991466979873176135600670874807 10131795236894275219484353056783002287856997829778 34784587822891109762500302696156170025046433824377 64861028383126833037242926752631165339247316711121 15881863851331620384005222165791286675294654906811 31715993432359734949850904094762132229810172610705 96116456299098162905552085247903524060201727997471 75342777592778625619432082750513121815628551222480 93947123414517022373580577278616008688382952304592 64787801788992199027077690389532196819861514378031 49974110692608867429622675756052317277752035361393 62107673893764556060605921658946675955190040055590 89502295309423124823552122124154440064703405657347 97663972394949946584578873039623090375033993856210 24236902513868041457799569812244574717803417312645 32204163972321340444494873023154176768937521030687 37880344170093954409627955898678723209512426893557 30970450959568440175551988192180206405290551893494 75926007348522821010881946445442223188913192946896 2200230144375
(more or less)