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Mumbai physicists uncover link between Lord Shiva, Mona Lisa
Hemali Chhapia| TNN | Jul 10, 2016, 06.58 AM IST
HIGHLIGHTS
Mona Lisa
MUMBAI: The golden ratio, the number that best describes the proportions of Leonardo da Vinci's Vitruvian Man and Mona Lisa, wasn't as unknown a concept in India centuries ago as has been thought. Represented by the Greek letter phi, it has been a subject of study in the field of aesthetics and has relevance in both physics and maths. Of course, its presence is manifest in nature, from spiral galaxies to snail shells and from flowers to algae. Now, a study by physicists Vijay Singh and Praveen Pathak from the Homi Bhabha Centre for Science Education has found that the sub-continent accorded the number both a scientific and a spiritual meaning ages ago. Their paper was published in the latest edition of the prestigious European Journal of Physics.
While staring at a folk painting of Lord Shiva in Bhojpur, Bihar, the two physicists were struck by the fact that the crescent moon which adorned Shiva's head resembled a circle removed from a larger circle, with the ratio of their diameters close to 1.618, which is a rounding off of the golden ratio. It wasn't mere coincidence either.Their study suggests that the number repeatedly occurs in a class of problems involving an object's centre of mass (roughly speaking, the point where all of the mass of the object is concentrated) and may be omnipresent.
The golden ratio is of great interest to the fashion industry . A lingerie giant has declared actor-model Scarlett Johansson to possess an almost perfect figure and reality TV personality Kim Kardashian as a close runner-up -- all on the basis of the golden ratio. It has been popularized by thriller writer Dan Brown in his books, mainly The Da Vinci Code. Leonardo himself was enamoured of it.
Singh and Pathak did calculations that revealed a number of striking facts: an excised or truncated circle (a smaller circle removed from a larger circle) will be balanced exactly on the edge. To their amazement they found that all even-sided polygons -- a closed figure (on a plane) made by joining several line segments--had this property. When a smaller "self-similar" polygon is excised from the larger polygon, the latter stands balanced on the edge only if the ratio of the sides of the two polygons was the golden ratio. For any other ratio, the centre of mass (which indicates the balance point) is either inside the larger polygon or outside it, which implies that the polygon is unstable.
"Circles and polygons have been around since time immemorial. But such a simple fact has gone unnoticed," said Prof Singh, who is of Science Olympiad fame.
Digging into spiritual literature, Pathak and Singh found several references of balancing on the edge. The Katha Upanishad mentions that the path of spirituality is akin to balancing a scimitar precariously on the edge. The very notion of Paramhansa is one who is poised between the spiritual and the material, notes Prof Singh. He mentions allied notions such as the Chinese yin and yang and the Yogic ida and pingala.
Pathak and Singh then undertook an analysis of three-dimensional structures such as the sphere and cube.And also of the higher dimensional tesseract, mentioned so prominently in the movie Interstellar. They have also discovered a sequence of polynomials (a type of mathematical expression) yielding a series of irrational numbers (numbers with decimal parts that go on and on, without segments of the digits ever repeating) between phi (1.618) and 2. These may provide additional figures of merit for the fashion industry, notes Singh wryly .
K Subramaniam, the Centre Director of HBCSE which is part of the TIFR, pointed out that the golden ratio and the Fibonacci series have a close connection and as one goes down the series and picks any two consecutive numbers and divides one by the other, the result comes close to the golden ratio.
http://timesofindia.indiatimes.com/...a-Mona-Lisa/articleshow/53136104.cms?from=mdr
Hemali Chhapia| TNN | Jul 10, 2016, 06.58 AM IST
HIGHLIGHTS
- A study by physicists Vijay Singh and Praveen Pathak from the Homi Bhabha Centre for Science Education has found link between Lord Shiva and Mona Lisa
- The ratio of beauty appears in an old painting of Lord Shiva in Bihar
- Their paper was published in the prestigious European Journal of Physics
MUMBAI: The golden ratio, the number that best describes the proportions of Leonardo da Vinci's Vitruvian Man and Mona Lisa, wasn't as unknown a concept in India centuries ago as has been thought. Represented by the Greek letter phi, it has been a subject of study in the field of aesthetics and has relevance in both physics and maths. Of course, its presence is manifest in nature, from spiral galaxies to snail shells and from flowers to algae. Now, a study by physicists Vijay Singh and Praveen Pathak from the Homi Bhabha Centre for Science Education has found that the sub-continent accorded the number both a scientific and a spiritual meaning ages ago. Their paper was published in the latest edition of the prestigious European Journal of Physics.
While staring at a folk painting of Lord Shiva in Bhojpur, Bihar, the two physicists were struck by the fact that the crescent moon which adorned Shiva's head resembled a circle removed from a larger circle, with the ratio of their diameters close to 1.618, which is a rounding off of the golden ratio. It wasn't mere coincidence either.Their study suggests that the number repeatedly occurs in a class of problems involving an object's centre of mass (roughly speaking, the point where all of the mass of the object is concentrated) and may be omnipresent.
The golden ratio is of great interest to the fashion industry . A lingerie giant has declared actor-model Scarlett Johansson to possess an almost perfect figure and reality TV personality Kim Kardashian as a close runner-up -- all on the basis of the golden ratio. It has been popularized by thriller writer Dan Brown in his books, mainly The Da Vinci Code. Leonardo himself was enamoured of it.
Singh and Pathak did calculations that revealed a number of striking facts: an excised or truncated circle (a smaller circle removed from a larger circle) will be balanced exactly on the edge. To their amazement they found that all even-sided polygons -- a closed figure (on a plane) made by joining several line segments--had this property. When a smaller "self-similar" polygon is excised from the larger polygon, the latter stands balanced on the edge only if the ratio of the sides of the two polygons was the golden ratio. For any other ratio, the centre of mass (which indicates the balance point) is either inside the larger polygon or outside it, which implies that the polygon is unstable.
"Circles and polygons have been around since time immemorial. But such a simple fact has gone unnoticed," said Prof Singh, who is of Science Olympiad fame.
Digging into spiritual literature, Pathak and Singh found several references of balancing on the edge. The Katha Upanishad mentions that the path of spirituality is akin to balancing a scimitar precariously on the edge. The very notion of Paramhansa is one who is poised between the spiritual and the material, notes Prof Singh. He mentions allied notions such as the Chinese yin and yang and the Yogic ida and pingala.
Pathak and Singh then undertook an analysis of three-dimensional structures such as the sphere and cube.And also of the higher dimensional tesseract, mentioned so prominently in the movie Interstellar. They have also discovered a sequence of polynomials (a type of mathematical expression) yielding a series of irrational numbers (numbers with decimal parts that go on and on, without segments of the digits ever repeating) between phi (1.618) and 2. These may provide additional figures of merit for the fashion industry, notes Singh wryly .
K Subramaniam, the Centre Director of HBCSE which is part of the TIFR, pointed out that the golden ratio and the Fibonacci series have a close connection and as one goes down the series and picks any two consecutive numbers and divides one by the other, the result comes close to the golden ratio.
http://timesofindia.indiatimes.com/...a-Mona-Lisa/articleshow/53136104.cms?from=mdr
