Fibonacci's topics - tribe.net

Fibonacci and Finance

2007-12-23T18:26:15Z

I learned recently that Fibonacci was one of the pioneers of the math behind moder day finance. Does anyone know if there is any connection between the world of finance and the golden mean? Is there any connection between the the golden mean and GOLD?

posted in Fibonacci - 1 reply

Hmmm... I wonder...

2007-09-17T14:45:04Z

What would it take for me to become moderator of this tribe?

posted in Fibonacci - 2 replies

Fib. in nature

2006-10-08T14:27:00Z

Look closely at a pine cone...you will fine the sequence in the spines that form the cone starting at the top....

posted in Fibonacci - 0 replies

Fibonacci Retracements

2006-01-08T05:43:23Z

Can someone tell me about this?

posted in Fibonacci - 1 reply

The Prehistoric Alignment of World Wonders

2005-12-02T13:30:50Z

Blow your mind:
http://home.hiwaay.net/~jalison/index.html

Exerpts:
--"Great circles are straight lines that go all the way around the center of the earth. The equator is a great circle. Meridians of longitude that cross over the north and south poles are also great circles."

--"Easter Island, Nazca, Ollantaytambo, Paratoari, Tassili n'Ajjer and Giza are all aligned on a single great circle. Additional ancient sites that are located within one tenth of one degree of this great circle include Petra; Perseopolis; Khajuraho; Pyay, Sukothai and Anatom Island."

--"The relationship between the distances from Angkor Vihear to the Great Pyramid and from the Great Pyramid to the Nazcan Hummingbird is also a precise expression of φ:

4,754 x 1.618 = 7,692

Because the Hummingbird and Angkor Vihear are antipodal sites, with a distance between them of one-half of the circumference of the earth, two Golden Section relationships between these three sites are shown by the circumference of the earth along the line of ancient sites."

--"Percentage of circumference:__First three digits of Fibonacci numbers:
Angkor to Giza: 19.1%________#137: 191... (Prime)
Giza to Nazca: 30.9%_________#138: 309...
Nazca to Angkor: 50.0%_______#139: 500...

Distance between sites:_______First five digits of Fibonacci numbers:
Angkor to Giza: 4,754 miles____#359: 47542... (Prime)
Giza to Nazca: 7,692 miles_____#360: 76924...
Nazca to Angkor: 12,446 miles__#361: 12446..."

--"Easter Island is triangular and the three volcanic peaks on Easter form an isosceles triangle with an apex angle of 108° and base angles of 36°. The ratio between the length of the base and the lengths of the sides is φ (6.8 miles x 1.618 = 11 miles)."

--"The straight line distance, through the Earth, from Angkor Wat to Easter (7,574 miles), plus the straight line distance from Easter to Macchupicchu (2,522 miles), equals the great circle distance from Angkor Wat to Easter (10,096 miles).

The straight line distance from the Great Pyramid to Easter (7,566 miles) is three times the straight line distance from Easter to Machupicchu (2,522 miles).

The straight line distance from Easter to its antipodal point in the Indus Valley (7,924 miles), which is also the diameter of the Earth, is 3.1416 times the straight line distance from Easter to Machupicchu (2,522 miles), a precise expression of π.

Since the circumference of the Earth is also 3.1416 times the diameter of the Earth, the straight line distance from Easter to Machupicchu times π² equals the circumference of the Earth."

--"As the Earth rotates on it’s axis, the Equator remains aligned, but the line of ancient sites describes a sine wave as a result of it’s tilt relative to the Equator. The line of the ecliptic may be observed describing a similar wave by spinning a globe that has a line of the ecliptic.

The wavelength is equal to the circumference of the Earth. The amplitude of this wave, measured from the middle of the wave (the equator), is 30° of latitude. Recall that the 30th parallels are ½ of the height of each hemisphere, or ½ of the radius of the Earth.

Since the height of the wave is equal to ½ of the Earth’s radius, the ratio between the wavelength and it’s amplitude is 4π. Measuring the amplitude from the top of the wavelength to the bottom (from 30° N to 30° S), the amplitude is equal to the radius of the Earth, and the ratio between the wavelength and the amplitude is 2π."

--"The old urban centers on the Eastern Seaboard of the U.S are in nearly perfect alignment.

This great circle line crosses through the middle of Washington DC and the middle of Boston, and it crosses right over the middle of New York City. It also crosses over Philadelphia and the Baltimore waterfront. The azimuth of this line as it crosses over NYC is 52°, which is also the angle of the sides of the Great Pyramid.

The alignment crosses between Teotihuacan and Cholula in Mexico and just as this alignment crosses into Mexico from the gulf it crosses over the ancient city of El Tajin and the pyramid of niches. The alignment also crosses over Baalbek, Lebanon and just north of the ancient city of Troy. The alignment also crosses over Stonehenge. The azimuth of the alignment as it crosses over Stonehenge is 72° west of due north and 72° east of due south, which is not the same as the primary alignment of Stonehenge itself. However, the alignment from the center of Stonehenge to the center of the heel stone is 52° east of due north, which is the same as the azimuth of this global alignment as it crosses over New York City and the same as the angle of the Great Pyramid.

In addition to the cities on the Eastern Seaboard and the ancient sites listed above, this alignment also crosses over a number of other major cities of the modern era, including Mexico City, the national capital of Mexico; Mobile, Alabama; Atlanta, Georgia; London, the national capital of England; Lille, France, Stuttgart and Munich in southern Germany; Zagreb, the national capital of Croatia; Belgrade, the national capital of Serbia; Sofia, the national capital of Bulgaria; Beirut, the national capital of Lebanon; Damascus, the national capital of Syria; and Riyadh, the national capital of Saudi Arabia."

posted in Fibonacci - 2 replies

Fibonacci and phi as number bases

2005-11-11T19:35:21Z

There are interesting articles at

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibrep.html
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/phigits.html
and
http://en.wikipedia.org/wiki/Golden_ratio_base

regarding using the Fibonacci sequence and the ratio phi as bases for number systems, similar to binary, decimal, or hexadecimal. Fun stuff!

A Fibonacci-base number (and phi-base number) will have digits 0 and 1, and will not have any two consecutive 1s. All integers are representable as Fibonacci-base integers, and as terminating phi-based expansions.

posted in Fibonacci - 0 replies

Some things I was told about the Golden Mean

2005-11-11T18:53:58Z

I've been having a long chat with someone who is very well known and respected in the world of science and sacred geometry, but he is keeping a low profile so I wont say who he is.

I love the Golden Mean so some of the things he said . . well have a look.

He has this to say about the Golden Spiral and i wondered if anyone wanted to comment on it?

Firstly I asked:
What is it that the Fibonacci does not have that keeps you from respecting it equally amongst other spirals?

And his response:
It's nonsense. It's trivial. It's almost useless.

There is a whole world of really intriguing forms. Forms based on the Fibonacci numbers are just not interesting, because they're so trivial.

I don't mind if others are fascinated by the wallpaper, but I'm not. There is nothing wrong with the Fibonacci numbers, other than that they're "a dime a dozen". The whole thing is just plain wacko. Why people are so focused on this triviality is beyond me.

He are some other snippets:

1. The golden proportion is sterile, because it's narcissistic. It always circles itself in its own self-image, just like Narcissus in the famous myth of Greek godly mental illness. Narcissism, self-centeredness (as represented by the logarithmic spirals, including the golden spiral), is the antithesis of maturity and spiritual growth. It attracts children whose world includes only themselves and
their parents.

2. The golden spiral is sterile because it is _completely_
symmetrical, and never changes. It's the opposite of life, which is why it only shows up in the dead traces of where life used to be. It's not productive. Life is extraordinarily asymmetrical. I'm not referring to the fact that we have left-right symmetry and two arms, two eyes, etc. I'm talking
about the process of life, not a photograph. The process of life is utterly asymmetrical, starting from a helpless single fertile cell, and growing into billions of cells of an utterly unique being with free will. This is truly "the one and the many". It's exactly the opposite of the "gilded" frauds being promoted on the Internet.

3. The golden proportion is not either enormously important, nor worthless. It's a number. It's one of an infinite number of interesting numbers. It's not important in any particular way, compared to many other numbers, and numbers are not important at all compared to what they represent.

On the scale of importance, if healthy, natural cooking is a 10, and McDonald's Burgerbilge is a 1, then the golden proportion is a 2. Okay? It ain't going to poison you, but it doesn't provide much nutrition, either.

4. The nutburger that wrote the book on the golden proportion for Dover Publications was a religious fanatic. This kind of pseudo-scientific nonsense has been selling like hotcakes for about a century and a half since someone first decided to call the "narcissistic" spiral, golden. (Prior to the mid-1800's, neither the proportion nor the spiral were called "golden". The name was because fraudsters were trying to "turn lead into gold". Apparently, this con still works, because there are plenty of people on the Internet who are buying it. It's just plain sad.)

5. The idea of "a most beautiful proportion" is itself simply not true. This doesn't stop artists from believing in it, but it does frustrate people who know more.

And then he says . . . .

There are extraordinary beauties in mathematics, but you have to refine your eyes first, in order to see them. Most mathematicians that I know see mathematics as a kind of music, perhaps the highest form of art because of its extraordinary beauty. (Most non-mathematicians don't see any of this. But then, people who are tone-deaf don't enjoy music.)

posted in Fibonacci - 7 replies

new but dreamt of fib as a child

2005-08-22T14:01:38Z

anyone else have these sequence dreams?

posted in Fibonacci - 1 reply

Fibonacci Poetry

2005-07-18T09:22:08Z

(title) Fibonacci Inspired

(1) "ah,
(1) yes"
(2) she sighed
(3) and circled
(5) eyes down shoulders round
(8) suplicated rhythmic dancing
(13) articulated sweeping of souls to higher ground
(21) and, at that moment, body derailed from mind, train of thought lost, joy unimagined gained

© Copyright 1996 by David Alan Foster

Fibonacci, the Man:

Leonardo of Pisa, nicknamed Fibonacci, was a mathematician who lived in the thirteenth century (1175–1230). He was among the first to introduce Arabic numerals into Europe. For more than two-hundred years, his work “Liber Abaci,” was a leading reference in mathematics. (Any connection to Liberace?)

Counting syllables in each line, the sequence is: 1, 1, 2, 3, 5, 8, 13, 21, and so on, the subsequent number being the sum of the previous two numbers. It would continue: 34, 55, 89, 144… (imagine 144 syllables!?). While Fibonacci didn’t necessarily discover this curious sequence, his investigations about the sequence resulted in it being named after him.

I found (in a book, I‘m no bloody mathematician!) that the Sequence appears if you measure the sides of the rectangle enclosing the Parthenon, then divide the long side by the short side! The pattern appears often in nature: count the bumps on a pineapple, the spirals of the yellow center of a daisy, a pinecone…

posted in Fibonacci - 1 reply

Fibonacci triangles

2005-05-17T02:16:41Z

I did an interesting experiment - Based on "Fibonacci Squares" I draw triangles in a spiral pattern. The size of new triangle is in the size of the total sides of the triangles forming this side. The sequence of sizes I've got is:
1,1,1,2,2,3,4,5,7,9,...

that is: a(n) = a(n-2) + a(n-3).

posted in Fibonacci - 5 replies

fibonacci and music

2005-04-03T02:54:36Z

http://www.spiritofmaat.com/archive/jan4/williams.htm

the wonders of the universe are immense and all encompassing.

The fibonacci sequence even relates by ratio to the harmonic (overtone) series in music. Our cochlea is the same shape as the snail shell, contains the GOLDEN MEAN and resonates to the pentatonic scale as well the the harmonic series.

posted in Fibonacci - 0 replies

The Torch of Life

2004-12-25T19:38:37Z

;-)

Just sharing my art . . . drawn on the fibon sequence . . .
see image bank.

www.torchoflife.tribe.net
www.spirit-of-yggdrasil.com

posted in Fibonacci - 0 replies

favorite links

2004-10-23T21:58:52Z

List some of the best links explaining Fibonacci sequence, PHI ratio etc. Here is one

http://goldennumber.net/

;

posted in Fibonacci - 0 replies

The Golden Section

2004-06-29T18:29:47Z

Has anyone here read "The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture" by Gyorgy Doczi? The Fibonacci series is discussed here as one..erm..expression of the Golden Section.

http://www.amazon.com/exec/obidos/ASIN/0877731934/qid=1087979542/sr=ka-1/ref=pd_ka_1/102-6465875-6443331

posted in Fibonacci - 8 replies

Fibonacci Stairs

2004-06-11T22:34:45Z

Check the photo I posted from my trip to the Key West. It is from a light house on the main key. Also I heard Alfred Hitchcock would use the visual of the stair case either decending or ascending to foreshadow dread and angst.

posted in Fibonacci - 0 replies

meta fictional history

2004-06-02T01:14:20Z

A Snail named Fibonacci (aka The Golden Escargot)
By Jake Sanders

1
10
101
10110
10110101
1011010110110
101101011011010110101

My roommate hates snails. They eat the plants in her garden. I understand this. She steps on them. Crushes them beneath her foot. I notice what she would term their ‘petty remains’ when I come home from work. A trail of her loathing and wrath – left to dry out in the sun. I wonder if she understands that on the back of a snail, his shell, his home, is nature’s pattern – a logarithmic formation of life on this planet represented in ‘the spiral’.

I wonder does she understand that the very life she attempts to save – the math of seeds and roots and water and light is represented in the very same spirals she crushes underneath the heavy weight of her fury.

I wonder does she understand that many a philosopher; Euclid of Alexandria (the leading mathematics teacher of all time), Leonardo Pisano - better known by his nickname Fibonacci, Leonardo da Vinci, and Albrecht Dürer stared at the shells of snails to find the patterns of life, truth and philosophy particular to this planet. These truths still hold.

I wonder does she know that Luca Pacioli (1445-1517) studied the shells of snails to help reach his Divina proportione (On Divine Proportion) Pacioli's work influenced Leonardo da Vinci (1452-1519) and Albrecht Durer (1471-1528) and is seen in some of the work of Georges Seurat, Paul Signac and Mondrian, for instance.

I wonder does she know that on the back of these snails in the sequence of related triangles can also be found in great pieces of art expressed as the golden ratio, the golden section, the golden mean, the golden number – also known as Phi.

I wonder does she know that the same structural patterns and proportions are evident in Virgil's Aeneid and other Roman poets of the time.
I wonder does she know that Mozart's sonatas divide into two parts exactly at the golden section point in almost all cases or that The section on "The Violin" in The New Oxford Companion to Music, Volume 2, shows how Stradivari was aware of the golden section and used it to place the f-holes in his famous violins or that Baginsky's method of constructing violins is also based on golden sections or that in Beethoven's Fifth we find that the famous opening "motto" appears not only in the first and last bars (bar 601 before the Coda) but also exactly at the golden mean point 0·618 of the way through the symphony (bar 372) and also at the start of the recapitulation which is phi or 0·382 of the way through the piece, or that Bartók, Debussy, Schubert, Bach and Satie also applied the sequence to a great many of their works both musical and theoretical.

I wonder does she know the architect Le Corbusier deliberately incorporated some golden rectangles as the shapes of windows or other aspects of buildings he designed. One of these is the United Nations building in New York which is L-shaped.

I wonder does she know The Russian Sergie Eisenstein directed the classic silent film of 1925 The Battleship Potemkin (a DVD or video version of this 75 minute film is now available, both in PAL format). He divided the film up using golden section points to start important scenes in the film, measuring these by length on the celluloid film.

Does she know that a flower, its seeds and its petals – are arranged in this same optimal form. Nature knows these things. Does she know that her very hands represent the same sequence; 2 hands each with 5 fingers 3 parts separated by 2 knuckles. I do not think she knows any of this, or cares.

So in the end we kill life in order to save life and not always in that order. But what really is at hand here is the way we go about it. In the end we all are snails of some sort at heart slugging along, slowly, inch by inch, eating away other forms of life, leaving a trail of slim in our wake, slowly moving along with homes on our backs toward that day that a heavy foot crushes us for no good reason at all.

posted in Fibonacci - 4 replies

Cool Pic's Posted

2004-02-23T06:38:24Z

Just posted some new pic's in the tribe folder.

Anyone else have some neat stuff to share?

posted in Fibonacci - 2 replies

getting started

2004-02-23T06:15:16Z

I've been interested in Fibonacci numbers since HS, so I thought it might be nice to have a tribe to discuss the interesting properties of these numbers and the life of the eponymous Leonardo. I'll do my best to answer any questions anyone might have.

posted in Fibonacci - 6 replies

Suddenly I have a desire to go to Germany

2004-02-03T05:17:02Z

Heard about this wonderful summer conference in class today. Anyone want to go to Germany in July?

http://www.ams.org/mathcal/info/2004_jul5-9_braunschweig.html

posted in Fibonacci - 0 replies