Home / FORUM / All / News / ... / Sejarah & Xenology /
[Diskusi] Masalah Umum Xenology

[Reborn] Xenology....


Buat yang pertama kali masuk ke trit ini pasti bertanya-tanya dalam hati dan gundah gulana (apaan sih emoticon-Hammer ), Xenology itu sejenis monster, makanan, atau nama momod ya ? emoticon-Nohope

This is it...

Spoiler for "Xenology adalah":

Jadi pengetahuan apa aja yang termasuk Xenology?

Spoiler for "Pengetahuan dalam Xenology":

ada pertanyaan,,unek2,,atau hal yang pengen ditanyain silahkan kemari.. emoticon-Smilie
Thread Xenology ini terbuka untuk umum...gratiss emoticon-Stick Out Tongue Thread ini tentunya juga terbuka bagi siapapun yang meyakini suatu fenomena dalam Xenology itu eksis, ataupun yang tidak mengakuinya. Terkadang believer suatu fenomena juga membutuhkan penentang agar keduanya bisa berdiskusi yang sehat.

Spoiler for "Xenology = HOAX?":

Feel Free to post emoticon-Smilie
Happy Sharing....

Spoiler for ga ngerti gan...topiknya aneh dan bikin bingung:

Kalo pembaca thread menemukan Artikel menarik di Blog/Lounge mengenai Xenology...bisa dimuat/diposting disini untuk dibahas. Jangan lupa tambahkan beberapa opini pribadi atau tambahan comment...supaya enak untuk membuka diskusi..emoticon-Smilie

RULES Internal Thread Xenology

1. sebisanya jgn one liner yah.. emoticon-Big Grin
2. Kalo nemu artikel cantumin juga linknya yaemoticon-Malu (S)
3. biasakan multiquote ya emoticon-Smilie
4. Jangan posting emoticon doang...
5. jangan PI (udah kayak spectre Soccer Room aja nih emoticon-Big Grin )
6. No HOAX icon (only) without explanation emoticon-Bata (S)
7. Boleh SARA emoticon-Bingung (S)

NB : yang ga boleh itu mendiskreditkan SARA emoticon-Hammer
kalo ga boleh SARA, bingung juga nih.. tar ngebahas suku Maya, Inca juga ga boleh dong emoticon-Ngakak (S)
8. ngikut peraturan Kaskus dan Forum Edu yang lain...

Thread ini didukung oleh :

pakisal212 dan 12 lainnya memberi reputasi
Diubah oleh Phoenix17

Mystery in Fibonaci Number

Fibonaci Number

The Fibonacci numbers are Nature's numbering system. They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.


The sequence, in which each number is the sum of the two preceding numbers is known as the Fibonacci series: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, ... (each number is the sum of the previous two).

The ratio of successive pairs tends to the so-called golden section
(GS) - 1.618033989 . . . . . whose reciprocal is 0.618033989 . . . . . so that we have 1/GS = 1 + GS.

The Fibonacci sequence, generated by the rule f1 = f2 = 1 , fn+1 = fn + fn-1,
is well known in many different areas of mathematics and science.
However, it is quite amazing that the Fibonacci number patterns occur so frequently in nature ( flowers, shells, plants, leaves, to name a few) that this phenomenon appears to be one of the principal "laws of nature".


Fibonacci was known in his time and is still recognized today as the "greatest European mathematician of the middle ages." He was born in the 1170's and died in the 1240's and there is now a statue commemorating him located at the Leaning Tower end of the cemetery next to the Cathedral in Pisa. Fibonacci's name is also perpetuated in two streetsthe quayside Lungarno Fibonacci in Pisa and the Via Fibonacci in Florence.
His full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa. He called himself Fibonacci which was short for Filius Bonacci, standing for "son of Bonacci", which was his father's name. Leonardo's father( Guglielmo Bonacci) was a kind of customs officer in the North African town of Bugia, now called Bougie. So Fibonacci grew up with a North African education under the Moors and later travelled extensively around the Mediterranean coast. He then met with many merchants and learned of their systems of doing arithmetic. He soon realized the many advantages of the "Hindu-Arabic" system over all the others. He was one of the first people to introduce the Hindu-Arabic number system into Europe-the system we now use today- based of ten digits with its decimal point and a symbol for zero: 1 2 3 4 5 6 7 8 9. and 0
His book on how to do arithmetic in the decimal system, called Liber abbaci (meaning Book of the Abacus or Book of calculating) completed in 1202 persuaded many of the European mathematicians of his day to use his "new" system. The book goes into detail (in Latin) with the rules we all now learn in elementary school for adding, subtracting, multiplying and dividing numbers altogether with many problems to illustrate the methods in detail.

Fibonacci and Nature
Plants do not know about this sequence - they just grow in the most efficient ways. Many plants show the Fibonacci numbers in the arrangement of the leaves around the stem. Some pine cones and fir cones also show the numbers, as do daisies and sunflowers. Sunflowers can contain the number 89, or even 144. Many other plants, such as succulents, also show the numbers. Some coniferous trees show these numbers in the bumps on their trunks. And palm trees show the numbers in the rings on their trunks.

Why do these arrangements occur? In the case of leaf arrangement, or phyllotaxis, some of the cases may be related to maximizing the space for each leaf, or the average amount of light falling on each one. Even a tiny advantage would come to dominate, over many generations. In the case of close-packed leaves in cabbages and succulents the correct arrangement may be crucial for availability of space.

This is well described in several books listed here >>

So nature isn't trying to use the Fibonacci numbers: they are appearing as a by-product of a deeper physical process. That is why the spirals are imperfect.
The plant is responding to physical constraints, not to a mathematical rule.

The basic idea is that the position of each new growth is about 222.5 degrees away from the previous one, because it provides, on average, the maximum space for all the shoots. This angle is called the golden angle, and it divides the complete 360 degree circle in the golden section, 0.618033989 . . . .

If we call the golden section GS, then we have

1 / GS = GS / (1 - GS) = 1.618033989 . . . .

If we call the golden angle GA, then we have

360 / GA = GA / (360 - GA) = 1 / GS.

Below there are some examples of the Fibonacci seqeunce in nature.

Petals on flowers*
Probably most of us have never taken the time to examine very carefully the number or arrangement of petals on a flower. If we were to do so, we would find that the number of petals on a flower, that still has all of its petals intact and has not lost any, for many flowers is a Fibonacci number:

* 3 petals: lily, iris
* 5 petals: buttercup, wild rose, larkspur, columbine (aquilegia)
* 8 petals: delphiniums
* 13 petals: ragwort, corn marigold, cineraria,
* 21 petals: aster, black-eyed susan, chicory
* 34 petals: plantain, pyrethrum
* 55, 89 petals: michaelmas daisies, the asteraceae family

Some species are very precise about the number of petals they have - e.g. buttercups, but others have petals that are very near those above, with the average being a Fibonacci number.
One-petalled ...

One-petalled ...

Two-petalled flowers are not common.

Three petals are more common.

Five petals - there are hundreds of species, both wild and cultivated, with five petals.

Eight-petalled flowers are not so common as five-petalled, but there are quite a number of well-known species with eight.

Thirteen, ...

Twenty-one and thirty-four petals are also quite common. The outer ring of ray florets in the daisy family illustrate the Fibonacci sequence extremely well. Daisies with 13, 21, 34, 55 or 89 petals are quite common.

Ordinary field daisies have 34 petals ...
a fact to be taken in consideration when playing "she loves me, she loves me not". In saying that daisies have 34 petals, one is generalizing about the species - but any individual member of the species may deviate from this general pattern. There is more likelihood of a possible under development than over-development, so that 33 is more common than 35.

Flower Patterns and Fibonacci Numbers
Why is it that the number of petals in a flower is often one of the following numbers: 3, 5, 8, 13, 21, 34 or 55? For example, the lily has three petals, buttercups have five of them, the chicory has 21 of them, the daisy has often 34 or 55 petals, etc. Furthermore, when one observes the heads of sunflowers, one notices two series of curves, one winding in one sense and one in another; the number of spirals not being the same in each sense. Why is the number of spirals in general either 21 and 34, either 34 and 55, either 55 and 89, or 89 and 144? The same for pinecones : why do they have either 8 spirals from one side and 13 from the other, or either 5 spirals from one side and 8 from the other? Finally, why is the number of diagonals of a pineapple also 8 in one direction and 13 in the other?

Are these numbers the product of chance? No! They all belong to the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. (where each number is obtained from the sum of the two preceding). A more abstract way of putting it is that the Fibonacci numbers fn are given by the formula f1 = 1, f2 = 2, f3 = 3, f4 = 5 and generally f n+2 = fn+1 + fn . For a long time, it had been noticed that these numbers were important in nature, but only relatively recently that one understands why. It is a question of efficiency during the growth process of plants.

The explanation is linked to another famous number, the golden mean, itself intimately linked to the spiral form of certain types of shell. Let's mention also that in the case of the sunflower, the pineapple and of the pinecone, the correspondence with the Fibonacci numbers is very exact, while in the case of the number of flower petals, it is only verified on average (and in certain cases, the number is doubled since the petals are arranged on two levels).

The explanation which follows is very succinct. For a much more detailed explanation, with very interesting animations, see the web site in the reference.

In many cases, the head of a flower is made up of small seeds which are produced at the centre, and then migrate towards the outside to fill eventually all the space (as for the sunflower but on a much smaller level). Each new seed appears at a certain angle in relation to the preceeding one. For example, if the angle is 90 degrees, that is 1/4 of a turn, the result after several generations is that represented by figure 1.

Of course, this is not the most efficient way of filling space. In fact, if the angle between the appearance of each seed is a portion of a turn which corresponds to a simple fraction, 1/3, 1/4, 3/4, 2/5, 3/7, etc (that is a simple rational number), one always obtains a series of straight lines. If one wants to avoid this rectilinear pattern, it is necessary to choose a portion of the circle which is an irrational number (or a nonsimple fraction). If this latter is well approximated by a simple fraction, one obtains a series of curved lines (spiral arms) which even then do not fill out the space perfectly (figure 2).

In order to optimize the filling, it is necessary to choose the most irrational number there is, that is to say, the one the least well approximated by a fraction. This number is exactly the golden mean. The corresponding angle, the golden angle, is 137.5 degrees. (It is obtained by multiplying the non-whole part of the golden mean by 360 degrees and, since one obtains an angle greater than 180 degrees, by taking its complement). With this angle, one obtains the optimal filling, that is, the same spacing between all the seeds (figure 3).

This angle has to be chosen very precisely: variations of 1/10 of a degree destroy completely the optimization. (In fig 2, the angle is 137.6 degrees!) When the angle is exactly the golden mean, and only this one, two families of spirals (one in each direction) are then visible: their numbers correspond to the numerator and denominator of one of the fractions which approximates the golden mean : 2/3, 3/5, 5/8, 8/13, 13/21, etc.

These numbers are precisely those of the Fibonacci sequence (the bigger the numbers, the better the approximation) and the choice of the fraction depends on the time laps between the appearance of each of the seeds at the center of the flower.

This is why the number of spirals in the centers of sunflowers, and in the centers of flowers in general, correspond to a Fibonacci number. Moreover, generally the petals of flowers are formed at the extremity of one of the families of spiral. This then is also why the number of petals corresponds on average to a Fibonacci number.
GDP Network
© 2021 KASKUS, PT Darta Media Indonesia. All rights reserved
Ikuti KASKUS di