View Full Version : The Golden Ratio and the Universe

rosie.johnson

2009-Jan-27, 06:04 PM

We are always hearing about how the golden ratio seems to be a design feature of practically everything on earth, so is it demonstrated out there in the universe? Can we identify patterns that are governed by the golden ratio within astronomical phenomena?

astromark

2009-Jan-27, 06:30 PM

We are always hearing ... The Golden Ratio and the Universe .

Can we identify patterns that are governed by the golden ratio within astronomical phenomena?

... Welcome Rosie... The rules of this universe seem to be set. Like the speed of light and the ratio of negative and positive mater. Is this what you are asking...

Then the answer is yes. They seem to be across the universe as the same...

If this is not what you are asking, please explain ?

hhEb09'1

2009-Jan-27, 06:46 PM

The golden ratio (http://en.wikipedia.org/wiki/Golden_ratio) ϕ is (1 + sqrt(5))/2, or 1.6180339887498948482... according to usoft calculator.

The ratio of two consecutive Fibonacci numbers gradually approaches the golden ratio, and the Fibonacci numbers crop up all the time in nature, mostly in plant growth patterns.

The ratio of the orbital periods of Earth (http://solarviews.com/eng/earth.htm)(365.256 days) and Venus (http://solarviews.com/eng/venus.htm)(224.701 days) is 365.256/224.701, or 1.6255..., which is close to ϕ. It's even closer to 13/8, or 1.625, the ratio of 13 and 8, two consecutive Fibonacci numbers.

Swift

2009-Jan-27, 11:22 PM

By the way rosie.johnson, welcome to BAUT.

alainprice

2009-Jan-28, 12:40 AM

The golden ratio (http://en.wikipedia.org/wiki/Golden_ratio) ϕ is (1 + sqrt(5))/2, or 1.6180339887498948482... according to usoft calculator.

Oh, thanks for that. I checked it and it is perfect!

I use the golden ratio in acoustics. When you build a speaker, the ideal shape for a rectuangular prism of a box is the golden ratio. It helps to avoid standing waves inside the enclosure.

Likewise, if you want to place the speakers best within a room, we sometimes divide the length and width of the room by the golden ratio and use the intersects as the speaker positions.

Basically, in the audio world, the golden ratio is used as the ideal way to break up measurements.

We use 0.618 : 1 : 1.618

It's also close to the ratio of mph to km/h.

Cougar

2009-Jan-28, 02:15 AM

We are always hearing about how the golden ratio seems to be a design feature of practically everything on earth, so is it demonstrated out there in the universe? Can we identify patterns that are governed by the golden ratio within astronomical phenomena?

That is an excellent question, Rosie. Welcome to the board!

I've also been intrigued since I heard of this "golden ratio," said to have some special significance. As hhEb09'1 has shown, there are some special qualities, beyond the more subjective design and feng shui (http://en.wikipedia.org/wiki/Feng_shui) utilizations. :)

What struck me the most was the fact that the golden ratio is the solution to a simple algebraic equation. When you square this number, you get exactly 1 more than the number.

x2=x+1

Make it a simple quadratic... (http://en.wikipedia.org/wiki/Quadratic_equation)

x2-x-1=0

To which there are two solutions, as previously noted, with a difference of exactly 1. :cool:

Oh, woops, that's not an astronomical phenomenon that you were asking about. Hmm.... :think:

Josh

2009-Jan-28, 02:28 AM

Check my sig. Heh

The golden ratio is found all over the place. It is used frequently in art and architecture (some well known art examples are Da VInci's Ventruvian Man, the Mona Lisa, Michelangelo's Holy Family and as i recall, the ratio of the base to the height of the great pyramid in Egypt approaches the golden ratio).

Examples from nature are the nautilus shell, pine cones, pineapples, sunflower seeds, arms of spiral galaxies, even the way rabbits procreate is based on the golden ratio. The number of bees (males, females, queen, worker, drone...) in a colony is governed (perhaps governed is too strong a word?) by the golden ratio. Even parts of your body follow the golden ratio.

It's everywhere I tell ya!

astromark

2009-Jan-28, 06:37 AM

The spiral arms of a Galaxy?

.... which one,? A ratio of 1. 1.618.... where ? To what ?

Oh dear me...

Thanks to the postings of others I now understand your question; You were not asking about the way things are in the universe at all. ie; The speed of light and expansion rates across the universe. From what others have contributed it is I who does not understand this ridiculous notion of mathematical significance or is that... ( insignificance )...

Numerical equations, Numbers are only of any relevance here on planet earth and involving people. We and only we have attributed mathematical numerology to all we see around us. This universe does not have a golden rule of numerical balance or any other sort of numerology for that mater. Do you really think that there might be some sort of golden rule. Never broken and always adhered to across the universe ? and who dare I ask set this rule and over See's its implementation.?

Oh dear me.... where, oh where did this come from. ?

The golden ratio ϕ is (1 + sqrt(5))/2, or 1.6180339887498948482... according to usoft calculator.

and yes I see all those wondrous 'connections' to things real and imagined...

What I do not see is any science.

At this moment I resolve this as nonsense.

and as you all know, I do not mind being wrong. So would one of you please fill in the gaps for me and explain what this is all about. Thank you.

alainprice

2009-Jan-28, 01:19 PM

Yo Astro, aren't you being a bit harsh?

We're being asked if the golden ratio shows up in the universe, not if it rules the universe.

One direction hinted thus far is the shape of spiral arms. I have yet to look up any references.

Delvo

2009-Jan-28, 02:26 PM

The golden ratio is found all over the place.But mostly or entirely in cases of biological origin, which isn't physics or astrology or such.

It is used frequently in art and architectureThese are products of human minds, so they indicate something about our mental processes, but not about the laws of physics or astronomical phenomena.

Examples from nature are the nautilus shell, pine cones, pineapples, sunflower seeds... even the way rabbits procreate is based on the golden ratio. The number of bees (males, females, queen, worker, drone...) in a colony is governed (perhaps governed is too strong a word?) by the golden ratio. Even parts of your body follow the golden ratio.I know some of this is for real, but have some doubts about the others. For example, if you start with a golden-ratio rectangle and add a line splitting it into two pieces where one pieces is a square with all sides equal to the original rectangle's short sides, the other piece is another golden rectangle, and if you do that again and again, you make a rectangular spiral which matches the spiral form of seashells and ram horns. But where does it come into the other things? What measurable quantity, divided by what other measurable quantity, yields this ratio, in each case? How much did quantities that didn't come out quite right need to be "rounded off" to hit this target? In how many of these cases is it a real golden function driving these results, rather than just a coincidence?

In particular, the human body has lots of different ratios in it, and they all vary from person to person. What parts show the golden ratio in their sizes or some other measurable quantity? What makes them any more noteworthy than the other body-part ratios such as 3 (foot length divided by width) and 2.5 (head height to hand width) and 1.whatever (finger length to metacarpal length) and 1 (iris diameter to finger width) and 4.5 (femur length to hand width)? What about differences in some such ratios between groups by age, race, health, and such? What about seemingly random variations between individuals even within every such group, like my longer-than-usual clavicles, ribs, and thumbs and shorter-than-usual spine? What fraction of the population must be within what range of the golden ratio, for it to count as an example of the standard human form being "based on" the golden ratio?

I have an image file showing a sketch of a human face in the form of a bunch of straight lines connected at angles, sometimes more than two lines meeting at the same junction. It's supposed to be the most averaged human face, the basic theme from which any variations create any of our unique features. It's also supposedly based on the golden ratio, but the actual ratios of the line length ratios in it, and the ratios of the distances between the major junctions, are distributed all over, with the golden ratio being no more common or important than any other. I've seen a pretty good justification for a connection between the golden ratio and equilateral pentagons and the angle 72° (although I don't remember what it is), but that shape (or even fragments of it and its internal diagonals) and that angle also don't show up with any particular prominence in this image. We're just supposed to believe the golden ratio is in there somewhere because it's said to be, but nobody ever seems to have heard of a process by which the image was supposedly derived from the golden ratio.

And since our recent ancestors had different faces from ours, what ratios did our whole lineage's faces evolve through on the way to this form, and why would our species be any more golden-ratio-based than other animals whose faces are completely different? It just doesn't make any sense.

Sometimes the lists of places the golden ratio is said to come up, with causality implied as if it's not just a coincidence but the ratio is actually built in to the process of how the things got that way, remind me of the way psychics and astrologers and such talk. I need to see verifiable details and justification in order to buy any new examples.

arms of spiral galaxiesHow does this one work? It's the only one I've seen alleged that doesn't come from biological origins (including human-made architecture and such as a subset of "biological origins").

ravens_cry

2009-Jan-28, 02:40 PM

Donald in Mathmagic Land (http://www.youtube.com/watch?v=P_ssR7M5Px0&feature=related) spends a considerable portion discussing the Golden Ratio, among other things.

As for myself, I like using it when I am designing fantasy architecture.

jniemann

2009-Jan-28, 03:19 PM

The spiral arms of a Galaxy?

.... which one,? A ratio of 1. 1.618.... where ? To what ?

Oh dear me...

Thanks to the postings of others I now understand your question; You were not asking about the way things are in the universe at all. ie; The speed of light and expansion rates across the universe. From what others have contributed it is I who does not understand this ridiculous notion of mathematical significance or is that... ( insignificance )...

Numerical equations, Numbers are only of any relevance here on planet earth and involving people. We and only we have attributed mathematical numerology to all we see around us. This universe does not have a golden rule of numerical balance or any other sort of numerology for that mater. Do you really think that there might be some sort of golden rule. Never broken and always adhered to across the universe ? and who dare I ask set this rule and over See's its implementation.?

Oh dear me.... where, oh where did this come from. ?

and yes I see all those wondrous 'connections' to things real and imagined...

What I do not see is any science.

At this moment I resolve this as nonsense.

and as you all know, I do not mind being wrong. So would one of you please fill in the gaps for me and explain what this is all about. Thank you.

Its not nonsense at all - you would do well to actually acquaint yourself with this topic. "The Golden Ratio" by Mario Livio is a good introduction.

There is also a reasonably good wikipedia article on it:

http://en.wikipedia.org/wiki/Golden_ratio

When people claim that golden ratio appears in nature in such things as Nautilus shells, Hurricanes and Galaxies, they are probably referring to the golden spiral - a specific type of logarithmic spiral which can be constructed by taking a rectangle and recursively dissecting it according to the golden ratio.

In polar co-ordinates, the golden spiral is given by r=phi^4*theta

A typical example of how to construct a golden spiral:

http://www.geocities.com/robinhuiscool/Goldenratio.html

In the case of a nautilus shell, the logarithmic spiral shape arises because the nautilus has evolved an efficient way of adding new chambers in order to grow. (Growth proportional to size). However, contrary to popular belief, when measurements of actual nautilus shells have been made, it turns out that they don't conform to a golden spiral, although they are a type of logarithmic spiral.

As far as galaxies go, M51 is said to be an example of a galaxy that conforms closely to a logarithmic spiral. Whether or not it actually conforms to a golden spiral is another matter ...

hhEb09'1

2009-Jan-28, 04:22 PM

It's also close to the ratio of mph to km/h.1.609344, exactly :)

cjameshuff

2009-Jan-28, 05:21 PM

We are always hearing about how the golden ratio seems to be a design feature of practically everything on earth, so is it demonstrated out there in the universe? Can we identify patterns that are governed by the golden ratio within astronomical phenomena?

Its occurrence on Earth is a bit exaggerated. You can approximately match a Fermat spiral to seashells and spiral galaxies, but it's not the only curve that does so. However, it does fall out naturally from plant growth, in the packing arrangement of cells and larger structures like seeds.

Astromark: Are you claiming that the ratio pi is also a fabrication? Just more useless numerology? How about e? Your rant could be just as easily applied to these.

It is not at all inconceivable that phi could show up in more fundamental places. For example, it appears in math related to Penrose tilings, infinite, non-periodic tilings that have 5-fold symmetry, fractal nature, which can be viewed as a projection of a 5 dimensional lattice onto 2 dimensions, and which have non-local characteristics somewhat reminiscent of aspects of quantum mechanics.

http://www.ams.org/featurecolumn/archive/ribbons.html

http://www.ams.org/featurecolumn/archive/penrose.html

Tensor

2009-Jan-28, 05:28 PM

1.609344, exactly :)

Geee, where did you find that at? :whistle:

Argos

2009-Jan-28, 05:59 PM

Astromark: Are you claiming that the ratio pi is also a fabrication? Just more useless numerology?

The Golden ratio is not a fabrication, for sure. But, undeniably, it has fascinated scores of mystics throughout the ages.

I canīt think of any relationship of the Golden Ratio with astronomical/astrophysical facts. Kepler struggled to find such a relationship in his time.

astromark

2009-Jan-28, 06:22 PM

I do hope we have not frightened 'Rosie' away...

Thank you's for the efforts shown and I feel encouraged and not alone in my observation of spiral cellular growth and galactic structures... It all makes perfect sense that a ratio can be found in that sort of structure. Yes I am well aware of the ratio of PIE involving the number of times a circumference is divided by a diameter. Like Douglas Adams I see the error of humanities foolishness. [(not 3.14. but 1.)]:) I still point to the fact that nature builds as it needs to and by the very nature of gravity and rotational velocity... The unfurling of a 'fern frond' is not mathematically correct. As the spiral structure of galactic mass is governed not by 'rules' of mathematical nonsense, but by the gravitational effect of its own making.... I stand by my view. You can find a common law. That is broken more than its not. Random coincidence. This is how I see it and do not expect adherence to my view, just tolerance of it will do.

So my answer to Rosie's question is NO. No such golden rule is to be found. Only humanity finds the need to adhere to mathematical insanity. Look what we have done with time... The universe dose not care.

Josh

2009-Jan-28, 10:25 PM

Sometimes the lists of places the golden ratio is said to come up, with causality implied as if it's not just a coincidence but the ratio is actually built in to the process of how the things got that way, remind me of the way psychics and astrologers and such talk. I need to see verifiable details and justification in order to buy any new examples.

Don't get me wrong here. I'm not attributing the numerous places people find phi to some sort of divinity or anything. Like pi, I do think it's found more frequently, though, than other ratios you discribed (like 4.5 - femur length to hand width).

Dr Stephen Marquardt (MD from UCLA, Chief of Facial Surgery at UCLA, Professorships at Loma Linda University and U. of Southern California - that's all I know about him and, while seemingly esteemed at UCLA, i don't know if he also believes that we didn't go to the moon, or if he hurts small animals or not :p) has done research into the mathematics of beauty. His research claims that people who are considered universally good looking, have faces that are in proportion to phi. Does it mean something that the relationship found is phi? Perhaps not. It could be coincidence (and I'm okay with it if it is) but it could be that there is some sort of math (which is, afterall, the language of the universe) we haven't yet found that relies on these ratios.

While I've no vested interest in the answer being one way or the other, I simply find it interesting that the number pops up over and over. Seeing mathematical relationships between things is how a lot of human progression occured. Seeing the relationships and trying to understand it is, I think, an integral part of science and the human condition.

As for the other question about how/why the spiral arms of a galaxy might form using phi ... I don't have an answer. I did find a pretty picture (http://apod.nasa.gov/apod/ap080517.html) though, so all is well (especially if you're a finite element analyst - because we all know it's about the pretty pictures and not the numbers hehe).

ravens_cry

2009-Jan-28, 10:37 PM

It is interesting though that we find things that use it beautiful. We find other things beautiful, but its use in much architecture is fascinating, even if only from a human psychology perspective. If it isn't to be found in the universe, why do we find this specifically beautiful? If anything, that makes this even more intriguing.

rosie.johnson

2009-Jan-30, 01:59 PM

Wow! I only asked a simple question or so I thought. Thank you for your contributions, some pertinent, some very interesting and some - more information than was actually asked for. Interesting that biology is not viewed as physics. I view everything that there is in existance as based on physics.

So, some spiral galaxy formations only. Thank you everyone.

closetgeek

2009-Jan-30, 04:48 PM

In particular, the human body has lots of different ratios in it, and they all vary from person to person. What parts show the golden ratio in their sizes or some other measurable quantity?

Delvo, I admit, I only heard of the Golden Ratio from that book Davinci Code. I am not claiming this is fact just relay what I read in a fiction book. Supposedly it's at certain dividing points in the body. From the top of your head to your belly button and from your belly button to your toes, shoulder to elbow and elbow to finger tip (same with hip to knee, knee to toe) are all supposedly divisible to the golden ratio. I am sorry if you weren't seriously asking for more examples.

My question is, when these numbers come up in all the different examples in nature on Earth and the universe, do they always conclude exactly or is there a margine of error?

Nick Theodorakis

2009-Jan-30, 06:10 PM

Donald in Mathmagic Land (http://www.youtube.com/watch?v=P_ssR7M5Px0&feature=related) spends a considerable portion discussing the Golden Ratio, among other things.

...

Would you believe that's one of the first things I thought of upon reading this thread, even though I haven't seen that movie since ca. 1970? It's nice to see it's still available for viewing someplace.

Nick

Sam5

2009-Jan-30, 06:45 PM

We are always hearing about how the golden ratio seems to be a design feature of practically everything on earth, so is it demonstrated out there in the universe? Can we identify patterns that are governed by the golden ratio within astronomical phenomena?

Interesting. This question comes up from time to time in art and cinema.

The old Academy format was 4:3 or 1.33 to 1.

Wide screen ranges from 1.5 to 2.5 to 1.

Old TV were 4:3, but most newer ones are 16:9 = 1.77

See movie formats:

http://en.wikipedia.org/wiki/Aspect_ratio_(image)

http://fotogenetic.dearingfilm.com/golden_rectangle.html

http://www.tvsleuth.com/education/widescreen-televisions-and-the-golden-rectangle/

http://en.wikipedia.org/wiki/List_of_film_formats

Robert Tulip

2009-Feb-02, 11:01 AM

Some slightly silly-seeming claims about phi built in to the solar system are at http://solargeometry.com/Geometry.htm It looks if you manipulate numbers you can find anything.

Delvo

2009-Feb-02, 07:41 PM

Here's that line-face thing that's supposed to have the golden ratio in it somewhere, but in which nobody can point out where it actually is or why it's more important than any of the other various ratios you can find in there.

My theory on this thing, based partially on the order in which I heard these bits of information about this image, is that first someone came up with it by superimposing various people's pictures and connecting the dots, and then someone else later came along and abused the observation by slapping the golden-ratio sticker on it.

metaphi

2009-Feb-18, 02:54 AM

Everything is fractal at both large and small scales, I found this pogram quite interesting, its as if even coastal lines and the shapes of countries are almost directly in line with a dodecahedron map (directly related to the Phi ratio).

http://members.telering.at/t.faltejsek/

Take a look through the gallery section and have a go on the software.

I reckon this in combination with google earth would be such a great tool for mapping plate tectonics, fault lines ect, I also belive that this mapping and the phi ratio has something to do with gravity. Take a quick look at images of the lunar poles on google too, the impact craters seem to follow a faint dodecahedron/spiral like shape, evidence showing a pattern in gravity pulling meteors to the surface??

http://dsc.discovery.com/news/2006/10/20/gallery/moonice2_zoom.jpg

www.myspace.com/metaphi - music I make :)

Murphy

2009-Feb-19, 05:58 PM

@ metaphi, Unfortunately what you seem to be talking about is pseudoscience nonsense. That site is just talking about a slightly updated version on the old Lay Line myth (see http://en.wikipedia.org/wiki/Ley_line).

Once it starts talking about mystical energy lines from the Pyramids at Giza and making statements like "No one can explane gravity", you know you are in deep New-Agey pseudoscience stuff. This sort of thing is also connected with some really whacky theories about Alien spaceships and UFO landing sites, etc, I'd say look at these things will a lot of scepticism.

astromark

2009-Feb-19, 06:37 PM

Good grief !... I can hardly with hold myself... Fantasy built on lies. All of it. Utter and complete nonsense.

Woo woo stuff at its very best... NO ! There are not grid like lines criss crossing the planet. Close the maths book and go outside. Look around you. You will not find Donald Duck like numerics engulfing your environment. Its true that some mathematical symmetry can be made to fit nature... Its not true that its all like that. Its not. Humanity has attached our numerical mathematical nonsense to reality. This solar system does not do the maths... It does just what ever... There are no patterns. None... My face is not in sink to some mathematical grid like pattern... Oh no I do not... :)way outside the look.

We are not even able to express the number of times a radii fits into a circumference accuratly... I would argue we are not so cleaver. " Pie should equal 1., but I am on my own there..." D Adams.:)mark.

Sam5

2009-Feb-19, 07:33 PM

Pie Grid:

http://www.kitchenu.com/shop/product.aspx?sku=1844

Murphy

2009-Feb-20, 04:08 PM

Pie Grid

Hehe :lol:

mugaliens

2009-Feb-21, 09:49 PM

Interesting. This question comes up from time to time in art and cinema.

The old Academy format was 4:3 or 1.33 to 1.

Wide screen ranges from 1.5 to 2.5 to 1.

Old TV were 4:3, but most newer ones are 16:9 = 1.77

Speaking of art and cinema, the most often quoted dimensions of the oo-la-la-ist female movie stars is 36-24-36.

36/24 = 1.5, which is again close to the Golden Ratio.

No wonder we find it appealing...!

hhEb09'1

2009-Feb-21, 10:12 PM

Speaking of art and cinema, the most often quoted dimensions of the oo-la-la-ist female movie stars is 36-24-36.

36/24 = 1.5, which is again close to the Golden Ratio.

No wonder we find it appealing...!100-62-100cm, even better

Stroller

2009-Feb-21, 11:32 PM

This essay by Landscheidt is interesting. Not all of it is astronomically relevant.

http://plasmaresources.com/ozwx/landscheidt/pdf/TheGoldenSection_ACosmicPrinciple.pdf

For numerical patterns in the larger scale structure of the universe, I find Ray Tomes work on harmonics fascinating, though it's regarded by some as pseudoscience.

http://www.bautforum.com/against-mainstream/63081-harmonics-theory.html

WayneFrancis

2009-Feb-23, 01:40 AM

Pie Grid:

http://www.kitchenu.com/shop/product.aspx?sku=1844

took me about 15 seconds to get this...I didn't read your post before I clicked on the link and was wondering why I was looking at this then went back and read the post...all 2 words of it and almost spat out the sip of coke I just took when I started to laugh.

Robert Tulip

2009-Feb-24, 06:51 AM

the golden ratio is the solution to a simple algebraic equation. When you square this number, you get exactly 1 more than the number. x2=x+1 Make it a simple quadratic... (http://en.wikipedia.org/wiki/Quadratic_equation) x2-x-1=0 To which there are two solutions, as previously noted, with a difference of exactly 1. :cool: Oh, woops, that's not an astronomical phenomenon that you were asking about. Hmm.... :think:This illustrates the natural beauty of the golden ratio. x2=x+1 => x = (x+1)/x = 1/x + 1 To which the only solution is phi = 1.618 = 0.618 + 1 by the quadratic formula

metaphi

2009-Feb-24, 05:14 PM

Okay then, forget i even mentioned anything, what i am talking about is all pseudoscience then. @ Astromark i wasnt saying that our numerical measurement of our reality is what governs reality, humans, through detailed examination of what is around us, have thought up laws that fit the nature of our environment.

I am just very interested in phi as everything i have looked at can be releated to it in some way, pick any thing and there will be some part of it that can be explained using phi. Suppose this could be said about any thing, but i think this ratio could be used to solve more of the universe's unsolved mysteries. I am not 'New-age' but i am very open to new ideas, unlike alot so called scientist who seem to have the opinion set in stone. I Might not post on here again, all i was looking for was abit of a disscussion about phi and astronomy. On the Phi Grid thing nonsence or not, who has proven this right or wrong? otherwise i consider it niether science or pseudoscience. Other things that got me thinking about a grid, Saturns hexagonal storm at its pole?

astromark

2009-Feb-24, 06:34 PM

You got what you wanted didn't you ? A discussion. I happen to agree that this phi thing can be found almost everywhere... and thank you for your clarity on this. Your opening ' Quote; " i wasn't saying that our numerical measurement of our reality is what governs reality, humans, through detailed examination of what is around us, have thought up laws that fit the nature of our environment."

But do not fell put off by my and other responses, its not personal. You and your question are welcome here.:) mark.

alainprice

2009-Feb-24, 07:39 PM

I am just very interested in phi as everything i have looked at can be releated to it in some way, pick any thing and there will be some part of it that can be explained using phi.

Really? If that's true, it IS significant.

The problem I see is that you yourself admit that parts, or pieces of observations match the golden ratio. Now you want to solve the universe's mysteries using it. That's a big jump, without any real reasoning.

Planck tried for years to incorporate his constant into classical physics. He met continued failure until Quantum Mechanics was formulated.

Sometimes, a piece of the puzzle won't help you, until you find the puzzle that it fits with.

Murphy

2009-Feb-24, 11:32 PM

I don't find Phi (φ) to be that much of an amazing number, it's used only very rarely in science (at least the science I'm familiar with), far more important "Golden numbers" are Pi (π) and e. They are used on a day to day basis by scientists and engineers around the world and are very significant (i.e. our civilization wouldn't function if we didn't understand them, whereas we would probably get by without knowing Phi).

BTW I just discovered something Phi, my PC monitor is 1680x1050, that's an aspect ratio of 1:1.6, it's appearing everywhere! :eek: :)

cjameshuff

2009-Feb-25, 01:35 AM

I don't find Phi (φ) to be that much of an amazing number, it's used only very rarely in science (at least the science I'm familiar with), far more important "Golden numbers" are Pi (π) and e. They are used on a day to day basis by scientists and engineers around the world and are very significant (i.e. our civilization wouldn't function if we didn't understand them, whereas we would probably get by without knowing Phi).

I think phi is better classed with things like sqrt(2)/2 and sqrt(3)/2. It does occur quite often in geometry...in the dodecahedron and icosahedron, for example, and in Penrose tilings. It crops up in many fullerene molecules, too...anywhere where there is 5-way symmetry, really. Not surprising:

2*cos(1/5*pi) = phi

1 + 2*cos(2/5*pi) = phi

2*cos(3/5*pi) - 1 = -phi

2*cos(4/5*pi) = -phi

2*cos(6/5*pi) = -phi

2*cos(7/5*pi) - 1 = -phi

1 + 2*cos(8/5*pi) = phi

2*cos(9/5*pi) = phi

1 + 2*sin(1/10*pi) = phi

2*sin(3/10*pi) = phi

2*sin(7/10*pi) = phi

1 + 2*sin(9/10*pi) = phi

2*sin(11/10*pi) - 1 = -phi

2*sin(13/10*pi) = -phi

2*sin(17/10*pi) = -phi

2*sin(19/10*pi) - 1 = -phi

It would be quite at home on a diagram like this one:

http://en.wikipedia.org/wiki/File:Unit_circle_angles.svg

edit: I do think it quite deserves a name of its own, simply due to the fact that 1 + 1/phi = phi, however.

metaphi

2009-Feb-25, 02:08 AM

Phi is directly related to a circle, you can fit any equal sided polygon within a circle?! every equal sided shape has a relation with phi?! Show me if im wrong. I am just trying to find things the don't relate to phi in any way so i can then explore them, I maybe obsessed with the ratio, maybe finding corolations with this ratio is unhealthy but maybe each and everyone's obsessions can be deemed as useful in some way.

I dont want to undermine 'true science' at the same time as exploring new thought.

SLIVKAisSoLiveOK K0hahaha

2010-Feb-25, 08:09 AM

So at the time I have not the time to read through the all of ye peoples quotes but as i skim through them I find yall ta seem like a solid group-o-folks. So I sincerely appologize in advanced for any contratdiction one would concure from my diction. If I completely go against your opinion it was with no intetions. Also if I repeate anyones already stated matters then I again appologize. this is doubtfull but I just dont know. Warning you may think I am a dumbass. Yes i am talking to you. Because I completely suck at math even simple arithmitik but I have bean known to spot Patterns naturaly. Autistik maybe idk.

Personaly I think the golden ration is the residual of Pie(or visa versa perhaps) and that it is also only one space of scientific notation away(its decimal place moved over a decimal place left or right idk). A tenth away. Which so Happens to be humans conception of a whole. 1, 10th, 100%, when the repeating scale starts over. I think of music when i think of this. I don't nessicarialy have the patients to check the math as you can tell by my spelling consideratioun, but when I put the two numbers besides eachother they realy seem to match into eachother.

Again i am sorry for the stupit noob response but I am kinda on a power trip right now and had to get something off my mind to see if anybody who knows what they are doing could pick up on it and perhaps even help me explain it. I feal like for my first response it is rude, crude, and out of place but thats kinda been my life. Then again I am talking on the internet and could for all i know be talking to absolutely no one. However this place seems legit so I know hopefully that the people will be understanding as well. One last word if I may, ( because it has profisized in mine and all of our philosophies that I will die tommorow if definantly not yesterday. Today is the only day right after yesterday, and we all die on a to-day.) My last words are "go ahead call me dumb, I've been working on the perfect response:)

01101001

2010-Feb-25, 04:37 PM

Welcome to BAUT Forum, SLIVKAisSoLiveOK K0hahaha

(Praise science for cut and paste.)

Personaly I think the golden ration is the residual of Pie(or visa versa perhaps) and that it is also only one space of scientific notation away(its decimal place moved over a decimal place left or right idk). A tenth away. Which so Happens to be humans conception of a whole. 1, 10th, 100%, when the repeating scale starts over.

Lost me. What sort of "residual" are you talking about?

"one space of scientific notation away" Explain?

Best to avoid thinking of 1, 10, 100 as magic numbers of any sort, because 10 is a pretty arbitrary number base that came into popularity because of the way primal fish fins happened to evolve into a pair of 5-fingered human hands.

Logarithms and powers, though, are interesting, almost magical.

astromark

2010-Feb-25, 06:46 PM

Phi is directly related to a circle, you can fit any equal sided polygon within a circle?! every equal sided shape has a relation with phi?! Show me if im wrong. I am just trying to find things the don't relate to phi in any way so i can then explore them, I maybe obsessed with the ratio, maybe finding corolations with this ratio is unhealthy but maybe each and everyone's obsessions can be deemed as useful in some way.

I dont want to undermine 'true science' at the same time as exploring new thought.

" A balanced diet is a pie in each hand..." Pie, phi, what are we doing here ?

If you look hard enough patterns can be found. Do they mean anything...NO !

Numbers. they are just numeric symbols of no significance to any and all.

As a star converts and expels energy to a point where gravity is defeated... Boom !

With no regard for numbers. Only we care. Lay down and let the feeling pass... or the numbers will engulf you... find a dark place, hide. (it works for me...):)

Uli Dinklage

2010-Nov-28, 10:54 PM

I don't find Phi (φ) to be that much of an amazing number, it's used only very rarely in science (at least the science I'm familiar with), far more important "Golden numbers" are Pi (π) and e. They are used on a day to day basis by scientists and engineers around the world and are very significant (i.e. our civilization wouldn't function if we didn't understand them, whereas we would probably get by without knowing Phi).

BTW I just discovered something Phi, my PC monitor is 1680x1050, that's an aspect ratio of 1:1.6, it's appearing everywhere! :eek: :)

(7*pi)/(5*e)= ?

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