The number that best describes the percentages of Leonardo da Vinci's Vitruvian Man and Mona Lisa, the golden ratio, was not as unknown a notion in India centuries ago as has been presumed. Represented by the Greek letter phi, it has relevance in both maths and physics and continues to be a subject of study in the area of aesthetics.
A study by Praveen Pathak and physicists Vijay Singh from the Homi Bhabha Centre for Science Education has found that the sub continent harmonized the amount both a scientific and a religious significance ages past. Their paper was published in the latest version of the prestigious European Journal of Physics.
Mumbai Physicists Find A Mathematical Link Between Mona Lisa And Lord Shiva
While staring at a folk painting of Lord Shiva in Bhojpur, Bihar, the two physicists were hit 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 was not just coincidence either. Their study indicates the number repeatedly happens in a category 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
Celebrity has been declared by a lingerie giant -model Scarlett Johansson to possess an almost perfect figure and reality TV style Kim Kardashian as a close runner up -- all on the foundation of the golden ratio. It is often popularized by thriller writer Dan Brown in his novels, mainly The Da Vinci Code. Leonardo himself was enamoured of it.
Singh and Pathak did calculations that shown a number of stunning facts: an excised or truncated circle (a smaller circle removed from a larger circle) will be balanced exactly on the edge. When a smaller "self-similar" polygon is excised from the larger polygon, the latter stands balanced on the edge only when the ratio of the sides of both polygons was the golden ratio. For another ratio, the centre of mass (which suggests the balance point) is either inside the bigger polygon or outside it, which suggests that the polygon is unstable.
"Circles and polygons have existed since time immemorial. But such a simple fact has gone unnoticed," said Prof Singh, who's of Science Olympiad acclaim.
Digging into religious literature, Pathak and Singh discovered several references of balancing on the edge. The Katha Upanishad mentions that the path of spirituality is akin to balancing a scimitar on the border. The very belief of Paramhansa is one who's poised between the religious and the material, notes Prof Singh. He mentions allied beliefs such as the Chinese yin and yang and the Yogic Ida and pingala.
Pathak and Singh subsequently undertook an analysis of three-dimensional structures such as cube and the sphere. And also of the higher dimensional tesseract, mentioned prominently in the picture Interstellar. These may provide added figures of merit for the fashion industry, notes Singh wryly.
K Subramaniam, the Centre Manager of HBCSE which is part of the TIFR, pointed out the golden ratio and the Fibonacci chain have a close link, and as one goes down the series and picks any two consecutive numbers and breaks up one by the other, the result comes close to the golden ratio.