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tommy Eternal Order Devil's Island 16543 Posts 
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Of late I have become fascinated by Fibonacci Numbers and The Golden Mean Etc. I think I will end up becoming like the fella in the movie “Pi”.
http://uk.youtube.com/watch?v=oQ1sZSCz47w It all seems to make sense of things that I have tried applying it to. Anyone else here fascinated by this magic?
If there is a single truth about Magic, it is that nothing on earth so efficiently evades it.
Tommy |
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IAIN Eternal Order england 18807 Posts
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It's the reason why playing cards, credit cards and similar have not changed in design (apart from that trendy single curved edge on some credit cards) - that golden ratio thing...
There's something about those cards that feel incredibly comfortable and natural to our hands proportionally speaking. It's also why the more symmetrical your face - the attractive you are perceived as being. You can test it quite easily with some photoshop-like software. Gimp is a free art package if you wish to try it.
I've asked to be banned
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Bill Ligon Inner circle A sure sign of a misspent youth: 6437 Posts
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Oh, yes, the Golden Ratio is very interesting. IAIN, round playing cards were marketed some years ago, but they didn't catch on at all. There is certainly something about the shape of playing cards that is pleasant to handle. I am sure the credit card companies are well aware of this.
Bill
Author of THE HOLY ART: Bizarre Magick From Naljorpa's Cave. NOW IN HARDCOVER! VIEW: <BR>www.lulu.com/content/1399405 ORDER: http://stores.lulu.com/naljorpa
<BR>A TASSEL ON THE LUNATIC FRINGE |
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MobilityBundle Regular user Las Vegas/Boston 120 Posts
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When I was first learning about math, I was very enthusiastic about the Fibonacci numbers and the golden mean. I was sure that there was some kind of deep significance of the relationship between them, and their prevalence in nature.
But eventually, somewhere around my third year in college as a math major, I had a somewhat anticlimactic realization: their prevalence is due to their simplicity. The Fibonacci numbers and the golden mean arise naturally from some very simple relations, like x^2 = x+1 (among many others). Because the relations are so simple, they come up in a lot of different places in nature and mathematics. And therefore, it's not so surprising to see these things in so many apparently disparate places. By contrast, there's an old conjecture (which has since been proved) called the "Monstrous Moonshine" conjecture. Without getting into details (because I don't understand them fully!), the conjecture relates properties of the so-called "Monster group," which is this ginormous (approx 10^54) collection of mathematical operations, to properties of another function that arises naturally in a context far-removed from the Monster group. The conjecture was called "Moonshine" because it was so improbable that these two fields should be related that some people thought it was mere coincidence. (Also, there's a story that someone once put up a bottle of whiskey to whoever solved the conjecture.) The point is, that's something really deep. To construct either the Monster group or the other function requires a lot of machinery, and it's really not clear that those things should overlap at all. But seeing all these instances of Fibonacci numbers or the golden mean is quite natural, as long as there's one of a handful of simple relations going on in the background. |
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Bill Ligon Inner circle A sure sign of a misspent youth: 6437 Posts
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I'm not a mathematician, but I am not mathematically illiterate, either. I just wonder about the simplicity. I would think that the very simplicity is profound. To illustrate, the hydrogen atom consists of one proton and one electron, the very essence, presumably, of simplicity. Yet, the whole universe is built on this simple atom. I have to admit this is more of an intuitive thing than a logical concept, but it seems very meaningful to me. Also regarding simplicity, consider fractals, the Mandelbrot set for example, built on iterating a simple function many times. I'm sticking my neck out here, but perhaps the Monstrous Moonshine conjecture will prove to involve so simple a relationship that it has been overlooked.
"There are no uninteresting numbers." -- possibly(?) Isaac Asimov Bill
Author of THE HOLY ART: Bizarre Magick From Naljorpa's Cave. NOW IN HARDCOVER! VIEW: <BR>www.lulu.com/content/1399405 ORDER: http://stores.lulu.com/naljorpa
<BR>A TASSEL ON THE LUNATIC FRINGE |
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tommy Eternal Order Devil's Island 16543 Posts
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I'm fascinated by just how it seems to make sense of so many things that I look at. You might think it silly to apply it to the stock market as the fella in the Pi film tries to do but look at this: These guys seem to make sense to me.
http://uk.youtube.com/watch?v=RE2Lu65XxTU
If there is a single truth about Magic, it is that nothing on earth so efficiently evades it.
Tommy |
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MobilityBundle Regular user Las Vegas/Boston 120 Posts
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Bill, I may be given to cynicism about this stuff too easily. But I don't think prevalence of a pattern due to simplicity is at all surprising.
For example, there's another sequence that we commonly see: 1, 2, 3, 4, 5... The analogue to the golden mean in this example is another number that's just as mysterious and deep: 1. I could go on an on about this sequence. It describes the evolution of the size of a population at a given time. It describes the progress made in performing many tasks, etc. And 1? Don't get me started about the beauty and depth of the number 1. But of course, nobody does, because the sequence and the number are *so* common that there's no sense of mystery. Adding 1 to things is so natural that nobody stops to think about it. My point is that adding two previous things is only slightly less simple, and therefore only slightly less common and slightly more deep. --------- Tommy, I confess I didn't watch the entire video. But of course, if the market were as simple as looking for Fibonacci patterns, these guys would have the cash to have better production values.
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Bill Hallahan Inner circle New Hampshire 3226 Posts
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Any sequence starting with two numbers that are summed to form the next number is a Fiobinacci sequence, not just the sequence shown in that video. The ratio of consecutive values in any Fiobinacci's sequence converges towards Phi as the sequence increases.
I think the most interesting Fiobinacci sequence is below. Each value P below is P to the next higher power. I had to use periods to space the exponents because of how the Magic Café formats text. Just pretend the periods are spaces, i.e. ignore them. P = 1 + Phi, which is approximately 1.618 ....2..3..4..5..6..7 1, P, P, P, P, P, P This forms a Fiobanacci sequence! In other words, the next power of Phi is the sum of the previous two lower powers of Phi! This is a remarkable result. There is much more that is cool about this. This is not the only remarkable sequence in mathematics, nor the only type of sequence that occurs in nature. I do agree, it is cool. If you like this type of things, study the relationship between Pascal's Triangle, raising binomial expressions to powers, combinatorics, and the binary system. These are all connected through Pascal's Triangle. Another cool sequence is one that involves powers of e, which is approximately 2.718281828. That raised to consecutive powers forms a curve where the area under the curve is equal to the slope of the curve at all positive values. That exponential sequence also occurs in nature. Perhaps the most amazing thing about this mathematics is that it was known so long ago, and yet relatively few people know, or care about it. Then again, there's just too much to learn today for any one person to know everything about anything.
Humans make life so interesting. Do you know that in a universe so full of wonders, they have managed to create boredom. Quite astonishing.
- The character of ‘Death’ in the movie "Hogswatch" |
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Magnus Eisengrim Inner circle Sulla placed heads on 1053 Posts
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Perhaps my favourite aspect of the Fibonacci sequence is Fibonacci's original problem. He asked us to imagine that we had a pair of newborn rabbits. If the rabbits are sexually immature for one month, then have precisely one pair of offspring at the end of every month after that, how many rabbits will you have in one year. (He assumes that the same rules apply for the offspring, that there is no mortality and that males and females are equally distributed.)
I'm pleased and surprised that a rabbit reproduction problem leads to so much interesting mathematics. John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.--Yeats |
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abc Inner circle South African in Taiwan 1081 Posts
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Which is why math confuses me and cooking doesn't. I can easily grasp how we can get from many rabbits to Phi.
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Magnus Eisengrim Inner circle Sulla placed heads on 1053 Posts
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Quote:
On 2009-01-03 14:08, IAIN wrote: Length to width on my bicycle cards is only 1.4. John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.--Yeats |
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balducci Loyal user Canada 227 Posts
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Math is cool, stay in school, learn it well ...
FWIW, in the news just today, the top 3 jobs this year are all math-related: http://www.careercast.com/jobs/content/JobsRated_10BestJobs
Make America Great Again! - Trump in 2020 ... "We're a capitalistic society. I go into business, I don't make it, I go bankrupt. They're not going to bail me out. I've been on welfare and food stamps. Did anyone help me? No." - Craig T. Nelson, actor.
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S2000magician Inner circle Yorba Linda, CA 3465 Posts
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Quote:
On 2009-01-07 21:53, Bill Hallahan wrote: This isn't true. The Fibonacci sequence starts precisely with 1, 1, . . . . The Lucas sequence is constructed like the Fibonacci sequence, but starts with 1, 3, . . . . What I find most interesting about the Fibonacci sequence is how it arises in nature: many plants contain bidirectional spirals, where the number of spirals in one direction and the number in the other direction are consecutive Fibonacci numbers. Examples are the eyes on a pineapple (8 spirals in one direction, 13 in the other), leaves on an artichoke (5 spirals in one direction, 8 in the other), and the center of a daisy (34 spirals in one direction, 55 in the other). |
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kcg5 Inner circle who wants four fried chickens and a coke 1868 Posts
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This is all so interesting, but I admit, I don't understand much of it I would like to hear bills retort to that.
The number 0 is interesting, just the concept of nothing was a great step in math.
Nobody expects the spanish inquisition!!!!!
"History will be kind to me, as I intend to write it"- Sir Winston Churchill |
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Scott Cram Inner circle 2678 Posts
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If all this Fibonacci stuff confuses you, check out goldennumber.net. The best place to start is the Phi basics page.
Here's Arthur Benjamin performing and e......th trick, starting at about 3 minutes into the video. BTW, don't believe everything you read, even...... numbers. |
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Kevin Ridgeway V.I.P. Indianapolis, IN & Phoenix, AZ 1832 Posts
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S2000magician...
Unless I am mistaken the Fibonacci actually starts with 0: 0+1=1 Which is what creates the next sequence: 1+1=2 Without starting at zero, why would it ever begin with two 1's...when two 1's are neither side by side nor in sequence? Kevin
Living Illusions
Ridgeway & Johnson Entertainment Inc Kevin Ridgeway & Kristen Johnson aka Lady Houdini The World's Premier Female Escape Artist www.LadyHoudini.com www.livingillusions.com |
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Magnus Eisengrim Inner circle Sulla placed heads on 1053 Posts
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Quote:
On 2009-01-08 12:31, Living Illusions wrote: Kevin, Remember the bunnies? In month 1, you have 1 pair. In month 2 you still have 1 pair because they are still sexually immature. In month 3 the bunnies give birth to their first pair of offspring, so you have 2 pair. That's why the sequence begins 1,1,2,... JOhn
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.--Yeats |
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Kevin Ridgeway V.I.P. Indianapolis, IN & Phoenix, AZ 1832 Posts
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John...0+1=1, 1+1=2 works perfectly under the definition of a sequence starting with two numbers that are summed to form the next number.
Also, your explanation with the rabbits is technically incorrect. The original pair of rabbits are also sexually immature, thus you don't get a pair right away, leaving you with zero additional pairs. In the West, the sequence was studied by Leonardo of Pisa, known as Fibonacci, in his Liber Abaci (1202)[8]. He considers the growth of an idealized (biologically unrealistic) rabbit population, assuming that: In the "zeroth" month, there is one pair of rabbits (additional pairs of rabbits = 0) In the first month, the first pair begets another pair (additional pairs of rabbits = 1) In the second month, both pairs of rabbits have another pair, and the first pair dies (additional pairs of rabbits = 1) In the third month, the second pair and the new two pairs have a total of three new pairs, and the older second pair dies. (additional pairs of rabbits = 2) The laws of this are that each pair of rabbits has 2 pairs in its lifetime, and dies. http://en.wikipedia.org/wiki/Fibonacci_sequence Kevin
Living Illusions
Ridgeway & Johnson Entertainment Inc Kevin Ridgeway & Kristen Johnson aka Lady Houdini The World's Premier Female Escape Artist www.LadyHoudini.com www.livingillusions.com |
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Scott Cram Inner circle 2678 Posts
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From the Wolfram Mathworld entry on Fibonacci Number:
Quote: The Fibonacci numbers are the sequence of numbers defined by the linear recurrence equation |
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Magnus Eisengrim Inner circle Sulla placed heads on 1053 Posts
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Quote:
On 2009-01-08 12:56, Living Illusions wrote: There are a couple of problems here. First, your example of having the first term as zero does fit the recurrence relation that defines the Fibonacci sequence, but it does not fit the standard initial term, as Scott Cram points out. Second, I am following Fibonacci in counting the total number of pairs of rabbits, not the number of births. I don't have a copy of Liber Abaci handy, but I do not believe that Fibonacci accounted for mortality in the way you suggest. Note also that, contrary to what you say, I did note that the first pair is sexually immature, which is why they don't reproduce until the end of the second month. Does anyone have a definitive source about the rabbit mortality? John
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned; The best lack all conviction, while the worst Are full of passionate intensity.--Yeats |
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Posted: Jan 3, 2009 05:37 pm 
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