Unsolved Mysteries - Fibonacci numbers in nature

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".

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.

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.


Human Hand

Every human has two hands, each one of these has five fingers, each finger has three parts which are separated by two knuckles. All of these numbers fit into the sequence. However keep in mind, this could simply be coincidence. Human Face

Knowledge of the golden section, ratio and rectangle goes back to the Greeks, who based their most famous work of art on them: the Parthenon is full of golden rectangles. The Greek followers of the mathematician and mystic Pythagoras even thought of the golden ratio as divine.

Later, Leonardo da Vinci painted Mona Lisa's face to fit perfectly into a golden rectangle, and structured the rest of the painting around similar rectangles.

Mozart divided a striking number of his sonatas into two parts whose lengths reflect the golden ratio, though there is much debate about whether he was conscious of this. In more modern times, Hungarian composer Bela Bartok and French architect Le Corbusier purposefully incorporated the golden ratio into their work.

Even today, the golden ratio is in human-made objects all around us. Look at almost any Christian cross; the ratio of the vertical part to the horizontal is the golden ratio. To find a golden rectangle, you need to look no further than the credit cards in your wallet.
Despite these numerous appearances in works of art throughout the ages, there is an ongoing debate among psychologists about whether people really do perceive the golden shapes, particularly the golden rectangle, as more beautiful than other shapes. In a 1995 article in the journal Perception, professor Christopher Green,
of York University in Toronto, discusses several experiments over the years that have shown no measurable preference for the golden rectangle, but notes that several others have provided evidence suggesting such a preference exists.
Regardless of the science, the golden ratio retains a mystique, partly because excellent approximations of it turn up in many unexpected places in nature. The spiral inside a nautilus shell is remarkably close to the golden section, and the ratio of the lengths of the thorax and abdomen in most bees is nearly the golden ratio. Even a cross section of the most common form of human DNA fits nicely into a golden decagon. The golden ratio and its relatives also appear in many unexpected contexts in mathematics, and they continue to spark interest in the mathematical community.
Dr. Stephen Marquardt, a former plastic surgeon, has used the golden section, that enigmatic number that has long stood for beauty, and some of its relatives to make a mask that he claims is the most beautiful shape a human face can have. The Mask of a perfect human faceEgyptian Queen Nefertiti (1400 B.C.)



An artist's impression of the face of Jesus based on the Shroud of Turin and corrected
to match Dr. Stephen Marquardt's mask

'Veyyil' selected for Cannes Film Festival - A milestone in Tamil Cinema history

Shankar had earned a good recognition as one of the best directors in India. However, he has a passion to produce films also and he used to encourage the talented technicians as directors.

This time he chose Vasanthabalan as the director of his film 'Veyyil' and that film was proved a big hit and won the critical acclaim. There were positive review from various newspapers and the media.

The film had completed centenary at various centres. Though the south Indian films try their best to earn a place in International Film Festivals, very few of them get an opportunity. This time, Veyyil had got the opportunity of screening at the 60th Cannes Film Festival. As the film is being screened abroad, the film makers gave sub-titles to it to enable the viewers the content of the dialogues and others.

It may be mentioned here that Cannes Film Festival is one of the best in the world. Over 30,000 movies would be screened and at least 1,000 directors, 5,000 producers, 4,000 distributors and an equal number of journalists from across the world would grace the festival to be held in France between May 16 to 27.

The title of this year's festival is 'All The Cinemas of the World'. According to information Veyil would be screened at 'Le Cinema DU Monde Theatre' at 6.30 pm on May 19.

The selection of a Tamil film in general and 'Veyil' in particular would remain a milestone in the history of Tamil cinema.

Sivaji - The BOSS --- music review

Here comes the music review of our BOSS
By Manoher Sreekumar ( NewYork, USA) with inputs from Arun Gopinath ( India )

It is 12:15 AM (EST, USA), April 3rd. A severe headache, didn’t sleep the previous night and have nothing in mind but just to hit the bed. 12:25 AM (EST), my Editor gives a call, checks on the status of the music review of Sivaji and hurriedly hangs the phone. Well, I switched on my music system and for the next four hours found myself doing nothing but listening to ‘The Boss’.

If you are just about to catch a flight or on your way to your office, I just have one line for you. “Sivaji audio is a magic, which needs to be experienced, cherished, remembered and revered for decades to come”, period.

Athiradee A.R.Rahman, Sayanora | Lyrics : Vali

I started with Athirade – had special instructions to start with this song, and took six replays before I could switch over to the next song. Rahman for Rajini – the two thalaivars of millions, will have millions more swinging, millions asking for once-mores and millions dumb stuck, when the song hits the silver screen. Rahman is unstoppable – thank the Lord, for making him pick this one for himself – “Billa, Ranga, Badshah thaan…evan pistol paesum bayshah thaan”. The female voice of Sayanora and the chorus are just great. Special mention for lyrics – its fun, frolic and frisk. Can someone tell me, is lyricist Vaali a 21 years old bloke out of New College?!

Balleilakka

S.P.Balasubramaniam, Raihanah, Benny & Chorus | Lyrics : Na.Muthukumar

Are you a big fan of his breath taking walks, his mesmerizing styles, his charming smile and his numerous trademark gimmicks, then rest assured you are just about to be taken on a memorable ride by the Superstar in this song. Hear this number and you cannot stop letting your imagination run wild, picturizing one of the biggest idols of all times just creating destruction on the 70mm screen. The intensity of SPB is too good to be written, he has sung as if he is making his debut with this album. Raihanah is refreshingly folky. Lyrics by Na.Muthukumar are just straight from heart! “Annan vantha TamilNadum America” – thaliva nee vararuthukku thaan nanga thavam kadakarom.

The Boss

Blazee, Naresh Iyer and Raqueeb Alam | Lyrics : Na.Muthukumar

Seven punch lines, three rappers and a three minute stunner. It would be a crime to review this piece more without the visuals. Written as a theme music for Superstar, the percussions used are definitely new to Tamil Film Music. Watch out for the last 30 seconds high finale! “Sachin adicha sixer thaan da, Sivaji adicha puncher thaan da”….lyricist Na.Muthukumar will hit big time if Rajinikanth’s fans lap up this song.

Vaaji Vaaji

Hariharan, Madhusree and chorus | Lyrics : Vairamuthu

A.R.Rahman might not be as innocent as he looks. He is a big timer teaser, starting the song with some mystic sounds resembling Buddhist musical notes. When you are all set expecting some slow paced melody, he changes the tempo with the chorus chanting “Aambal Aambal”….. “Muval Muval”. Well, if you are wondering what these words are, they are the two most researched words in Tamil now, after Vairamuthu used them in this song. The song sung by Hariharan and Madhusree is a classic example of a genius at work. Though it looks simple from outside, it has little bit of everything – Qawwali, Punjabi, Mediterranean and of course Tamil. (Maybe that is what the maestro himself is all about!)

Sahara

Vijay Yesudas, Gomathi Sree & chorus | Lyrics : Vairamuthu & Traditional lyrics of Thiruppaavai

Vijay Yesudas, Gomathi Sree & chorus | Lyrics : Vairamuthu & Traditional lyrics of Thiruppaavai A haunting irish pipe seamlessly transitions itself into a flute, with the mellifluous Vijay Yesudas bolstering it further to give the song a great start. Vijay has given his best to make the most of the big opportunity. His efforts have paid off. But the surprise element is Gomathi Sree, her voice resonate and reverberate as she recites the Thirupaavai, with a subtle guitar in the background. Yet another master stroke from the Mozart.

Sahana

Udit Narayan, Chinmayi | Lyrics : Vairamuthu.

If it was Munbe Vaa in 2006, then it is Sahana in 2007. Rahman just loves doing the soft melodies. But the best part about Rahman is that he is able to consistently break the bench marks he sets himself and keep pushing his music further to the next level with constant improvisation and re-inventions. He does it again this time with Sahana. Udit Narayan and Chinmayi are picture- perfect for the song, though Udit might need some more intensive Tamil classes to catch up. Rahman’s interlude is just the icing on the cake. Watch for the way Chinmayi signs off at end, talent written all over! Vairamuthu comes up with a masterpiece. It is said that Rajinikanth wished the poet personally for his work on this song.

Style

Rags, Tanvi, Suresh Peters, Blaaze | Lyrics : Pa.Vijay.

Have you heard of anything like this before in Tamil music….no. Has Rajini done anything as flauntingly flashy as this before…..no. But still the guts and imagination of Shankar and Rahman make them experiment here and in the process brings Hip Hop to Tamil audience. The song has been getting good reviews so far from various quarters, though it is expected to take off once it has Sivaji Rao Gaekwad shaking his leg. “Black or white, it really doesn’t matter!!”….hmm what does that mean….is there some hidden fact there. Pa.Vijay comes up with some very catchy lines to make it interesting.

The album

Looking back at the album, Shankar has succeeded in extracting the best out of Rahman, now the big question….will he succeed in extracting the best out of Rajini? Finally, for few frowners who are still not satisfied with the music, I have just this to say… “Rest in peace, you will be conquered!” And for the rest of the people who are still reading, Go get the CD, cause its Rahman who is rocking!! Go get the CD, cause there will be nothing left over!!

Indian Cricket Board interested in retaining Chappell in advisory capacity

At the end of the first leg of the BCCI meeting to review India's debacle in the World Cup, the board issued a statement recognising Greg Chappell's commitment and seeking his continuing assistance to Indian cricket though not in the capacity as coach. "Chappell emphasized the need to promote youngsters and concentrate on fitness and strength for the team to do well in fielding and running between the wickets. Sharad Pawar was of the opinion that Chappell could be associated with Indian cricket and help us implement our long term plans though he's no longer the India coach," the statement said.

Chappell presented his report to the committee where he refused to name any specific player or players as being the main reason for India's defeat. The statement said: "In his report Chappell confined himself to issues and did not make any reference to individual players. [Sanjay] Jagdale was also of the opinion that youngsters should be inducted into the team to improve our cricket."

Earlier, the Indian board's meeting to discuss the team's early exit from the World Cup had begun with all parties attending the meeting arriving at the board headquarters at Wankhede Stadium, Mumbai, well before the appointed time.

In the absence of any official statements from any of the people concerned, there was much speculation over the future of Chappell. Unconfirmed reports suggested that Chappell was being offered some position in Indian cricket, possibly even coach, but it has been reliably learnt that Chappell would not be leaving Mumbai on Friday night as earlier planned.

Niranjan Shah, the board secretary, appealed to the media not to speculate on what was being discussed at the meeting. "Is it so difficult to wait till Saturday evening," Shah asked presspersons as reported by AFP. "Such reports do not make our job easier."

"If I have to spend all my waking hours denying all that is appearing in the media, I will have no time to attend the meetings," he said in response to queries.

Chappell, who had announced on Wednesday that he would not seek an extension to his contract as the Indian coach, left the meeting at 11.50am IST waving and smiling at the media assembled outside the stadium. Two hours later, Rahul Dravid made his exit as well. Sanjay Jagdale, the team manager for the World Cup, was still at the meeting.