# The Golden Ratio

#### timothy posted more than 10 years ago | from the cradle-of-life dept.

676
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.

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.

You can purchase The Golden Ratio from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.

## Book Review: The Golden Shower (-1, Troll)

## stratjakt (596332) | more than 10 years ago | (#8202962)

## It works, sorta.. (0, Funny)

## grub (11606) | more than 10 years ago | (#8202970)

## Re:It works, sorta.. (-1, Troll)

## Anonymous Coward | more than 10 years ago | (#8203091)

## GOLDEN RATIO? MORE LIKE GOLDEN SHOWER (-1, Troll)

## Anonymous Coward | more than 10 years ago | (#8202974)

## golden ratio? (-1, Troll)

## Anonymous Coward | more than 10 years ago | (#8202978)

## I wrote a review.. (-1, Interesting)

## Tirel (692085) | more than 10 years ago | (#8202980)

## BUT DOES IT RUN LINUX (-1, Offtopic)

## SIG TR0LL (749566) | more than 10 years ago | (#8203033)

## From your english class? (4, Insightful)

## iota (527) | more than 10 years ago | (#8203138)

for my english class. hope you enjoy it.I presume you got an F. Since is a direct and obvious plagarism of the publisher's description of the book. (see: http://search.barnesandnoble.com/booksearch/isbnI

It's obvious, because it doesn't really say anything other than what can be related to the title of the book (which is not unusual for back-of-the-book descriptions)

It's direct, because, well -- I can search google for any sentence in your text and find it.

Lame.

## Actually, from the link listed... (-1, Troll)

## W32.Klez.A (656478) | more than 10 years ago | (#8202985)

You can purchase The Golden Ratio from bn.com.The link [bfast.com] says:

A new copy is not available from Barnes & Noble.com at this time.maybe the editors should check closer next time.

## Re:Actually, from the link listed... (0)

## RandBlade (749321) | more than 10 years ago | (#8203045)

## Re:Actually, from the link listed... (1, Troll)

## stratjakt (596332) | more than 10 years ago | (#8203076)

Do they get referrer bucks or some other such lame innernet moneymaking scheme?

## I HOPE A TURD LANDS IN YOUR MOUTH (-1, Flamebait)

## Anonymous Coward | more than 10 years ago | (#8203098)

## Q: What's the best part about 12 noon at slashdot? (-1, Offtopic)

## Anonymous Coward | more than 10 years ago | (#8202992)

A: It's 1700 GMT. That means all the Brits have finally given up pretending to work and gone home for the day. According to statistics, post quality soars over 30% on average.## I loved this book, until... (-1, Offtopic)

## Anonymous Coward | more than 10 years ago | (#8202994)

What the hell does a tortured bunghole have to do with radio?

## Re:I loved this book, until... (0)

## Anonymous Coward | more than 10 years ago | (#8203043)

## The Da Vinci Code (2, Informative)

## fee^ (94129) | more than 10 years ago | (#8202999)

## Re:The Da Vinci Code (1, Informative)

## Kenja (541830) | more than 10 years ago | (#8203061)

## Re:The Da Vinci Code (1)

## DR SoB (749180) | more than 10 years ago | (#8203294)

## Re:The Da Vinci Code (1)

## Thud457 (234763) | more than 10 years ago | (#8203329)

## Re:The Da Vinci Code (2, Insightful)

## Anonymous Coward | more than 10 years ago | (#8203081)

## Re:The Da Vinci Code (3, Insightful)

## wfolta (603698) | more than 10 years ago | (#8203186)

The Golden Ratio is carefully and deeply researched. The Da Vinci Codes is allegedly based on research, but the "research" behind it is recycling tired old conspiracy theories.

From his statements online and in his forward, methinks Dan Brown is trying to have it both ways: claim it's based on fact but use the plausible deniability of it being a fictional work. It is a gripping read, don't misunderstand me. But you have to remind yourself that it's totally fictional.

## Re:The Da Vinci Code (1)

## DR SoB (749180) | more than 10 years ago | (#8203321)

## Re: Da Shitty Code (2, Funny)

## Anonymous Coward | more than 10 years ago | (#8203191)

Provided we ignore

EVERY OTHER WRITER EVER.## How far is HURD behind release now? (-1, Offtopic)

## Anonymous Coward | more than 10 years ago | (#8203005)

## The Galaxy?? (4, Funny)

## Gorimek (61128) | more than 10 years ago | (#8203007)

## obligatory (0)

## Anonymous Coward | more than 10 years ago | (#8203203)

## Sad news ... Stephen King dead at 56 (-1, Offtopic)

## Anonymous Coward | more than 10 years ago | (#8203008)

I just heard some sad news on talk radio - Horror/Sci Fi writer Stephen King was found dead in his Maine home this morning. There weren't any more details. I'm sure everyone in the Slashdot community will miss him - even if you didn't enjoy his work, there's no denying his contributions to popular culture. Truly an American icon.

## Re:Sad news ... Stephen King dead at 56 (-1, Troll)

## Anonymous Coward | more than 10 years ago | (#8203131)

definitelynot on the New York Times, LA Times, or any other of those Commie-terrorist-loving lefty papers!!! I haven't watched FOX News but I'm sure at least they reported it! I can't believe the control the liberal media has over this country!!!!-AC (hint:doesn't stand for Anonymous Coward)

## Re:Sad news ... Stephen King dead at 56 (-1, Troll)

## mblase (200735) | more than 10 years ago | (#8203244)

## aw man (-1, Offtopic)

## Savatte (111615) | more than 10 years ago | (#8203024)

## The Golden Ratio (4, Funny)

## Anonymous Coward | more than 10 years ago | (#8203047)

## Mathematics not universal? (5, Insightful)

## s20451 (410424) | more than 10 years ago | (#8203055)

If mathematics are not universal, then the mathematical reasoning that can be conducted to deduce the laws of nature is also not universal. Hence, if a different civilization has different mathematics, they have different physical laws as well.

This is basically a postmodern viewpoint, that reality is socially constructed. This viewpoint has been largely derided by the scientific community, and has failed to replace science because it hasn't really offered a compelling alternative. The only way I can see it being true is if other civilizations don't "exist" in the universe as humans do.

Do a google search for Alan Sokal for a scientist's viewpoint of postmodern scientific criticism.

## Re:Mathematics not universal? (-1, Offtopic)

## Bongzilla (458471) | more than 10 years ago | (#8203170)

## Re:Mathematics not universal? (1)

## Trelane, the Squire (608266) | more than 10 years ago | (#8203197)

It's also an assumption to say that aliens would be about our size in body mass. Different size changes the way they would 'look' at the universe.

## Re:Mathematics not universal? (3, Insightful)

## s20451 (410424) | more than 10 years ago | (#8203303)

Then again, if they have no concept of "time" or "movement", then I would argue that they don't exist in the universe in the same way we do.

## Re:Mathematics not universal? (4, Funny)

## kfg (145172) | more than 10 years ago | (#8203220)

I kick them in the shin.

Then say, "Why did you do that?"

KFG

## Re:Mathematics not universal? (4, Insightful)

## Raindance (680694) | more than 10 years ago | (#8203232)

Rather, I'd set mathematics and logic equal (there's a respected tradition that does, see Bertrand Russell, Principia Mathematica). Then, to say that mathematics isn't the same across the universe, one would say that logic isn't the same across the universe.

Now, "Logic isn't universal" is a damn meaningless statement. It'd translate into "Logic cannot describe [timespace-area/context] X." Which is, of course, a logical assertion about X.

I think either the reviewer's portrayal of the argument or the argument itself is bogus.

RD

## Something I learned from Martin Gardner... (5, Informative)

## kzinti (9651) | more than 10 years ago | (#8203059)

x = 1 + 1/x

You'll get a quadratic with the solutions (1 +/- sqrt(5))/2, or 1.618... and -0.618...

## Re:Something I learned from Martin Gardner... (4, Interesting)

## product byproduct (628318) | more than 10 years ago | (#8203213)

On a calculator:

1) start with any number

2) press [1/x] [+] [1] [=]

3) GOTO 2

In other words this converges to the golden ratio! It takes a while, so normally you do this when you're bored.

## math is not universal? (3, Insightful)

## liquidpele (663430) | more than 10 years ago | (#8203060)

How could it not be?

Math is just a way of describing objects, forces, and interactions... how could you describe them differently??

## Re:math is not universal? (5, Insightful)

## greatmazinger (747174) | more than 10 years ago | (#8203124)

Math is just a way of describing objects, forces, and interactions..Ummm, no. That's not math. That's physics. Math is more abstract and one can do math without associating any of the concepts with "reality". One you use math to model reality, it becomes science and engineering.

## Re:math is not universal? (0)

## Anonymous Coward | more than 10 years ago | (#8203287)

## Re:math is not universal? (0)

## Anonymous Coward | more than 10 years ago | (#8203188)

## Re:math is not universal? (0)

## Anonymous Coward | more than 10 years ago | (#8203205)

## Different aliens (1)

## Trelane, the Squire (608266) | more than 10 years ago | (#8203250)

## Re:math is not universal? (1)

## robbway (200983) | more than 10 years ago | (#8203256)

For instance, math doesn't really need to add. The concept can be completely explained with the concepts of negative numbers and subtraction.

To get a real handle on the concept of different mathematics models, take the extremely difficult class of Abstract Algebra. It's called Algebra because it wraps itself around the ideas of open sets, closed sets, and operations as a generic concept.

## Movie (4, Informative)

## savagedome (742194) | more than 10 years ago | (#8203072)

## Re:Movie (4, Funny)

## ath0mic (519762) | more than 10 years ago | (#8203181)

:)

## Re:Movie (0)

## Anonymous Coward | more than 10 years ago | (#8203336)

As pointed out above, Phi is neat because it solves x=1+1/x, and just about any self-repeating shape (5-sided star, golden rectangle) has it. You can compute any of the Fibbonacci numbers with it directly (F(n)=((phi^n - phiC^n)/sqrt(5)) where phi is 1.617... and phiC is 1/phi, IIRC), and it has uses in generating realistic imagery in computer graphics.

## Pi the movie (4, Interesting)

## cryptochrome (303529) | more than 10 years ago | (#8203356)

Not bad (aside from one glaringly obviousl mathematical error). The thing that I mulled over the most was the proposition that a large integer could be a number of fundamental significance. In the movie it was 216 digits long. I had always figured all the really fundamental numbers were irrational. After thinking about it and looking up on the internet it seems there are actually only 6: pi, e, i, 1, 0, and phi (and arguably, -1). And the first five can be directly related with the equation:

e^(pi*i) + 1 = 0

phi is not directly related to the others in such a manner (In the movie the god number is somehow tied to both pi and phi). Although pi and phi both happen to be ratios that are also irrational. But to get back to my original point, the suggestion that any number of a truly fundamental significance besides 0 and 1 would be not only rational but an integer seems improbable.

## The Da Vinci Code (0, Offtopic)

## Mork29 (682855) | more than 10 years ago | (#8203074)

## Re:The Da Vinci Code (1)

## mblase (200735) | more than 10 years ago | (#8203209)

Da Vinci played a small part in all this fun Phi stuff, and evidence of it can be found in his paintings.He was far from the first, and I don't just mean Aristotle. The ancient Egyptians believed that this "sacred ratio" was important enough to embed in their art and constructions. Many Egyptian temples employ rectangluar archways designed according to the Golden Ratio (phi).

At the Great Pyramid of Giza, the ratio of the length of one side of the base to the perpendicular height of the pyramid is about 2/phi, making the slant height of the pyramid side proportionately equal to phi. The result is that each side of the pyramid is a Golden Triangle.

## Sounds like an interesting book (1, Funny)

## Anonymous Coward | more than 10 years ago | (#8203077)

1.618033988749894848204586834365638117720309179

## Why wouldn't math be known across the universe? (5, Insightful)

## ObviousGuy (578567) | more than 10 years ago | (#8203078)

Could there be some areas of mathematics that humans have discovered that has not been discovered by an alien race? Sure. Prior to Newton there was no calculus and so Kepler had to discover the period of planetary orbits using geometry and algebra. But this does not mean that Kepler would not have used calculus if it had been available to him, only that such a concept had not yet been thought of.

But counting and simple addition and subtraction are mathematical operations that are mastered even by animals. It is fairly condescending to assume that aliens could not even fathom those levels of mathematics.

## Re:Why wouldn't math be known across the universe? (4, Interesting)

## Sique (173459) | more than 10 years ago | (#8203233)

## Re:Why wouldn't math be known across the universe? (3, Insightful)

## Apostata (390629) | more than 10 years ago | (#8203241)

"It is fairly condescending to assume that aliens could not even fathom those levels of mathematics."And it's fairly narrow-minded to assume that another life form in the galaxy has a frame of perception that's even remotely similar to ours. This is more than just saying "what if they see in infra-red!", but rather to say that we feel mathematics is the de facto language of the universe because it (as with terrestrial life on Earth) doesn't yet have a competitor.

## Re:Why wouldn't math be known across the universe? (1)

## Suicyco (88284) | more than 10 years ago | (#8203263)

## What about aliens at the molecular level? (1)

## Trelane, the Squire (608266) | more than 10 years ago | (#8203288)

## Re:Why wouldn't math be known across the universe? (5, Interesting)

## arbour42 (731167) | more than 10 years ago | (#8203367)

Prior to Newton there was no calculusIn a fascinating book, a Hindu scholar and monk, Sri Tirthaji, discovered in the Hindu Veda scriptures the basis for our math system. There he found shortcuts for most all our math work - easy ways to do difficult long divisions in a matter of seconds, quadratic formulas, PI to over 32 digits, the Pythagorean theorem (much before the Greeks), derivatives, calculus.

Our math is actually from the Vedas, and the Arabs got it from them, and then spread it through the Western world. The Vedas are at least several thousand years old.

The book is called Vedic Mathematics or Sixteen Simple Mathematical Formulae from the Vedas [amazon.com] and can be found at amazon or used book stores.

It's one of the major works of genius of science. The first time i read it, it was shocking how advanced it was, and simple! Any division such as 1.748362 / 59487 can be done

long handed(pencil and paper) in a minute.Our math system, how it was discovered or invented, who knows and how far back, is absolutely brilliant.

## Re:Why wouldn't math be known across the universe? (1)

## mslinux (570958) | more than 10 years ago | (#8203372)

Could there be some areas of mathematics that humans have discovered...Math is not discovered, it's made up. One plus one is two because men made rules that make it that way. Also, you can use mathematical models to prove that math is not consistent... Read up on Godel's Theorems. The

onlything that makes math work are the rulesthat we all must accept(these are called axioms). If we do not accept the rules, then math doesn't add up... pardon the pun.## Thumbs up (1, Offtopic)

## haxor.dk (463614) | more than 10 years ago | (#8203092)

If you're looking for something a bit along the same lines, but sprinkled with history, religion and conspiracy, I can recommend "the Da Vinci Code" by Dan Brown.

## Numbers are numbers (4, Insightful)

## Wind_Walker (83965) | more than 10 years ago | (#8203121)

By the same nature, prime numbers are always prime. There exist a certain number of things (5, 7, 11, etc) and cannot be evenly divided. Period. We call them prime numbers, and we use our base-10 radix. Aliens could call them Borgolsmocks in their base-182, but the fact still remains that a Borgolsmock cannot be divided evenly.

And I firmly believe that no intelligence would survive for long without a knowledge of mathematics. Counting the days for crop rotation, the ability to evenly divide food among the tribe, and communication of the number of animals in a herd... mathematics will be generated in the evolution of any intelligent species.

And it is truly universal.

## Re:Numbers are numbers (1)

## Radix37 (670836) | more than 10 years ago | (#8203262)

Regardless of what radix used (10-based, hex, octal, etc) "6" of something is still "6".What if you used radix 37?

## Re:Numbers are numbers (1, Funny)

## Anonymous Coward | more than 10 years ago | (#8203337)

Please define the following in absolute, universal terms:

cannot:

be:

divide:

evenly:

## A god with a plan? (5, Interesting)

## mindstrm (20013) | more than 10 years ago | (#8203129)

The balance and beauty of nature and all that?

OF COURSE there is a pattern, and things work out. Look at evolution.

You take a puddle in the middle of nowhere.. it has an ecosystem in it with a perfectly balanced population (too many, it dries up, too few, they reproduce...). Would these little creatures say "Oh wow! Look how there is JUST enough water for each of us! There must be a GOD!".... silly, right?

Nature seems balanced in the world, becuase that world produced nature... they are intertwined, infinitely.

Irrational numbers only seem strange because of the way we choose to look at things... the fact that it doesn't reduce to some fraction in our counting system doesn't *mean* anything holy or significant....

The fibonacci series and the golden ratio are related? Sure are.

(The ratio of successive numbers in the fib. series approaches the golden ratio as you go upwards)

But it's not so weird, is it? A sunflower.. the way it grows, it builds on itself.. in a spiral... naturally following this series.

Is it some grand creator that made it that way, or is it just the plain, obvious way for something to grow?

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.

Until then, i'ts just nature.

## I LIKE YOUR STYLE, TROLL (0)

## Anonymous Coward | more than 10 years ago | (#8203172)

## Re:A god with a plan? (2, Funny)

## Geckoman (44653) | more than 10 years ago | (#8203281)

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:A god with a plan? (2, Interesting)

## danmitchell (691749) | more than 10 years ago | (#8203382)

Since I'm taking a class on general relativity this semester, I'll weigh in with a quote of Albert Einstein.

In other words, maybe nature is what it is because God created it that way, or maybe it is what it is because it

hasto be.## I rememeber this from... (5, Interesting)

## gpinzone (531794) | more than 10 years ago | (#8203133)

## Furniture design (5, Interesting)

## hulap0pr (562242) | more than 10 years ago | (#8203134)

## Re:Furniture design (1)

## cj79 (718594) | more than 10 years ago | (#8203247)

Case pieces (boxes, bureaus, etc...) appear more balanced and pleasing to the eye when the golden ratio is followed.Same can be said for centerfolds.

## This topic... (1)

## ArmenTanzarian (210418) | more than 10 years ago | (#8203152)

I just finished the somewhat overrated, but entertaining Da Vinci Code [google.com] which mentions this in addition to several other interesting. The presentation is that of fiction, which adds entertainment, but detracts from the believability.

Also the movie Pi [google.com], which I probably need not mention here, speaks of this to some length.

Final question being, does this book really add to my knowledge of the subject? I think I've heard all of the examples of where this ratio can be found in nature, is this guy just beating a dead horse? The review doesn't really imply that there's anything new here.

## muscle memory (1)

## Matey-O (518004) | more than 10 years ago | (#8203156)

## Re:muscle memory (0)

## Anonymous Coward | more than 10 years ago | (#8203237)

## Re:muscle memory (0)

## Anonymous Coward | more than 10 years ago | (#8203242)

## universal math? (4, Interesting)

## mblase (200735) | more than 10 years ago | (#8203159)

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.Yes and no. Mathematics is just a way of modelling things abstractly. Even things like counting from one to ten is a model for concrete objects, and provides a way of, say, making sure the number of cows you have today is the same as the number of cows you had yesterday. At the higher level, mathematics lets you model shapes, motion, acceleration, and gravitational collapse of entire stars.

The most common types of mathematics we use include decimal arithmetic (trading with money), algebra (solving for unknown quantities), and geometry (simplifying the world into abstract shapes). Hundreds of other branches of mathematics exist to model different things in different ways, and none of them are "right" -- they all are optimized for particular problem-solving.

With that in mind, I find it inconceivable that advanced civilizations on other planets would not have some kind of mathematics, and at least share the natural numbers with us (not necessarily base ten, though). If all you're doing is raising food for your family, then even arithmetic may be more than you need to bother with. But anything that involves abstract problem-solving, measurement, and/or exchange of goods for trade is going to need some kind of math. The models they use may bear no resemblance to the ones we use, but that doesn't mean it's not math.

## How does one dispute math as a universal concept? (2, Insightful)

## hellfire (86129) | more than 10 years ago | (#8203162)

I would think that math in some was is universal, in the sense that every sentient creature has to figure out a method of

counting. Some creatures count in base 10, others base six, maybe base 12. Other creates could figure out a counting base we haven't thought of yet. However, if they have a method of counting and measuring, I'm sure we'd have a method of translating their mathmatical models to our own, without too much trouble.Perhaps the definition of math here is different than mine? Thoughts?

## Opinion, Mr. Spock? (2, Funny)

## ackthpt (218170) | more than 10 years ago | (#8203163)

## who trusts this review... (-1, Troll)

## Anonymous Coward | more than 10 years ago | (#8203165)

## Definition FYI (3, Interesting)

## Prince Vegeta SSJ4 (718736) | more than 10 years ago | (#8203166)

The number 1.618..., which is half the sum of one plus the square root of five (1+SQRT(5))/2. This number was known in ancient times, and has many interesting properties in many fields. In Fibonacci series, the higher one goes in the series, the closer the ratio between a number and it's predecessor comes to the Golden Ratio.

From "The Technical Analysis of Stocks, Options & Futures" - William F. EngGeez, I never thought my Trading and /. would come together. Then again it is delving into the Uber Math Geek world - lol

## Awful (1)

## dubbayu_d_40 (622643) | more than 10 years ago | (#8203177)

## First-contact scenarios? (5, Insightful)

## bravehamster (44836) | more than 10 years ago | (#8203183)

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. ... 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.From what I understand, the vast majority of realistic first-contact scenarios postulated involve using mathematics as a common ground to bridge the language barrier. 1 + 1 equals 2 in every language on earth (except New Age holistic 1 + 1 = 3 crap). It makes sense and it works everywhere. It would be awfully damn hard to build a spaceship without mathetmatics, let alone trying to calculate launch trajectories or transfer orbits. Unless they had such an intuitive grasp of higher level mathematics that they don't even consider it worth talking about, I don't see how any species that had no concept of math could ever rise above the level of pointy sticks and sharpened rocks. And even then you'd probably want to keep track of how many rocks you had to make sure Lurg over there didn't *borrow* a few.

## Right you are! (0, Offtopic)

## davek99999 (749198) | more than 10 years ago | (#8203196)

## pi rules! 3.141592... (-1, Troll)

## Anonymous Coward | more than 10 years ago | (#8203215)

## Intelligent marketting strategy for stupid ideas (2, Funny)

## dtfinch (661405) | more than 10 years ago | (#8203231)

## Phi (5, Funny)

## Rupert (28001) | more than 10 years ago | (#8203240)

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.

## The real question is... (1)

## Eightlines (536572) | more than 10 years ago | (#8203252)

## Groklaw (-1, Offtopic)

## digitalchinky (650880) | more than 10 years ago | (#8203260)

## hmm.. (1)

## andy55 (743992) | more than 10 years ago | (#8203261)

Finally, Livio takes a shot at the idea that mathematics is a universal concept across the entire universe.This seems like a tall, tall order. I've been into math/geometry/visual related software [soundspectrum.com] for years now and am now transitioning into making my living off it. However, the fact that there are still many fundamental mysteries in mathematics always raises doubt on the things like our origins, God, and the universe. Pi is the best example of that. It's no puzzle to me why countless minds have tried to be the hero (or the mathematician version of one), to unlock pi's mystery, but no one has yet to really break through. The film

Piis an excellent and enjoyable film, and considers the magnitude (as well as the price) of unlocking pi's mystery.I'd like to day I'm open minded, but whew. Perhaps such things are more considerable when you start to consider all the various matter/energy theories floating around out there. There's still gigantic mysteries still out there for cosmology and physics (dark matter, open universe, dark energy, unification of gravity into the standard model), so I suppose we should never be too hasty to close the door on counterintuitive or far-fetched theories. I'd love to hear anyone who can paraphrase the thrust of this person's arguments, etc.

## math and humanity (3, Insightful)

## jstoner (85407) | more than 10 years ago | (#8203265)

Could a race become spacefaring without math? Could they develop the radio communications we could use to detect them? I suppose they could if the circumstances of their environment or adaptation (Low-gravity, bio-radio communications) allowed it.

But how would you arrive at the necessary conclusions without an abstracted intellectual framework like math? Maybe progress would just be slower.

Hmmm... makes you wonder what we're still missing.

## If you like math history (1)

## hey! (33014) | more than 10 years ago | (#8203268)

It covers a sampling of many of the great theorems and proofs of mathematics in a form that anyone with high school math can follow, as well as giving interesting insights into the personalities of the mathematicians (where this can be known). Most of them were, um eccentric. It is nice to know that Euler at least was well adjusted, if you couldn't exactly call him

normal.Euclid is represented twice here: once for his proof of the Pythagorean theorm and once for his proof of the infinitude of primes.

## Don't confuse Syntax for Content (4, Insightful)

## Master Switch (15115) | more than 10 years ago | (#8203276)

## Bullshit (0)

## Orion442 (739483) | more than 10 years ago | (#8203278)

## Debunking constants (4, Interesting)

## hcg50a (690062) | more than 10 years ago | (#8203301)

This doesn't sound exactly right.

I think it may be the case that writers have attributed the use of phi in art when there was no such intentional use by the artist.

But the very nature of phi makes it unlikely

notto appear in certain contexts.Same with pi.

The thing I love about math is that it has utterly nothing to do with reality or the universe or anything at all.

Typically, however, physicists make assumptions that match, more or less closely, to what is happening in the real world, so the conclusions from such assumptions match, more or less closely, to what is actually happening in the real world.

But there is no reason why some utterly alien intelligence can't make a set of assumptions that match

theirreality, which would be utterly alien to us, yet still valid, and still recognizable by mathematicians, if not physicists.This is the giant flaw at the end of the book Contact, by Carl Sagan. Ellie discovers a message in the constant pi, placed there by an intelligence. If this were a constant of physics, that would imply the existence of some incredibly advanced intelligence that engineered the universe to contain a constant with precisely that value. This is somewhat plausible, and I believe it was Sagan's intent.

But he picked pi, which actually has nothing at all to do with this or any other universe.

What kind of incredibly advanced intelligence can possibly engineer that? I can only think of One.

## The Golden Ratio in statistics (1)

## careysb (566113) | more than 10 years ago | (#8203316)

## The answer is 42! (1)

## MalaclypseTheYounger (726934) | more than 10 years ago | (#8203317)

6 X 9 = 42 in base 13.

## The Golden Ratio (0, Redundant)

## Anonymous Coward | more than 10 years ago | (#8203346)

golden mean(proportio divinaorsectio aurea), also called golden ratio, golden section, golden number or divine proportion, usually denoted by the Greek letter phi, is the number phi = (1 + sqrt 5)/2 = approx. 1.618033Two quantities are said to be in the Golden ratio, if "the whole is to the larger as the larger is to the smaller", i.e. if (a+b)/a = a/b. Equivalently, they are in the golden ratio if the ratio of the larger one to the smaller one equals the ratio of the smaller one to their difference: a/b = b/(a-b).

After simple algebraic manipulations (multiply the first equation with a/b or the second equation with (a-b)/b), both of these equations are seen to be equivalent to (a/b)^2 = a/b + 1 and hence a/b = phi.

The fact that a length is divided into two parts of lengths a and b which stand in the golden ratio is also (in older texts) expressed as "the length is cut in extreme and mean ratio".

The ancient Egyptians and ancient Greeks already knew the number and, because they regarded it as an aesthetically pleasing ratio, often used it when building monuments (e.g., the Parthenon). The pentagram so popular among the Pythagoreans also contains the golden mean. It is also sometimes used in modern man-made constructions, such as stairs and buildings, woodwork, and in paper sizes, however it is a myth that the European formats (such as A4, which is actually cut to 4 decimal places of sqrt 2) are cut in the golden mean. Recent studies showed that the Golden ratio plays a role in human perception of beauty, as in body shapes and faces.

A possible reason for its supposed attractiveness is shown by the Golden rectangle, which is a rectangle whose sides a and b stand in the Golden ratio. If from this rectangle we remove a square with sides of length b, then the remaining rectangle is again a Golden rectangle, since its side ratio is b/(a-b) = a/b = phi. By iterating this construction, one can produce a sequence of progressively smaller Golden rectangles; by drawing a quarter circle into each of the discarded squares, one obtains a figure which closely resembles the logarithmic spiral theta = (pi/2 log(phi)) * log r.

Since phi is defined to be the root of a polynomial equation, it is an algebraic number. It can be shown that phi is an irrational number. Because of 1+1/phi = phi, the continued fraction representation of phi is 1+1/(1+1/(1+...)) = [1; 1, 1, 1,

The number phi turns up frequently in geometry, in particular in figures involving pentagonal symmetry. For instance the ratio of a regular pentagon's side and diagonal is equal to phi, and the vertices of a regular icosahedron are located on three orthogonal golden rectangles.

The ratios of justly tuned octave, fifth, and major and minor sixths are ratios of consecutive numbers of the fibonnaci sequence making them the closet low integer ratios to the golden mean. James Tenney reconceived his piece For Ann (rising), which consists of up to twelve computer generated upwardly glissandoing tones, as having each tone start so it is the golden ratio (in between an equal tempered minor and major sixth) below the previous tone, so that the combination tones produced by all consecutive tones are a lower or higher pitch already, or soon to be, produced.

The explicit expression for the Fibonacci sequence involves the golden mean. Also, the limit of ratios of successive terms of the Fibonacci sequence equals the golden mean. From a mathematical point of view, the golden ratio is notable for having the simplest continued fraction expansion, and of thereby being the "most irrational number" worst case of Lagrange's approximation theorem. It is also the fundamental unit of the algebraic number field

Q(sqrt 5) and is a Pisot-Vijayaraghavan number.The golden mean has interesting properties when used as the base of a numeral system.

1. 6180339887 4989484820 4586834365 6381177203 0917980576 2862135448 6227052604 6281890244 9707207204 1893911374 8475408807 5386891752 1266338622 2353693179 3180060766 7263544333 8908659593 9582905638 3226613199 2829026788 0675208766 8925017116 9620703222 1043216269 5486262963 1361443814 9758701220 3408058879 5445474924 6185695364 8644492410 4432077134

## Lincoln's distorted texts (0)

## Anonymous Coward | more than 10 years ago | (#8203349)

Abraham Lincoln himself used Euclid's texts....This explains a lot, especially Lincoln's distorted views of North versus South....

## 1.61803399 (2, Informative)

## karmaflux (148909) | more than 10 years ago | (#8203363)

## 1.6?!! I THOUGHT THE RATIO WAS 9 TO 4?! (0)

## enigmals1 (667526) | more than 10 years ago | (#8203379)

Man where have I been... I guess I have to get this book now. I always thought it was 9:4 or 21/4 to 1. *shrug*