THE GLITTER OF THE GOLDEN RATIO – Part 2
(A presentation by Subbaram Danda)
In the past, GR was expertly deployed by sculptors and artists to portray human figures in aesthetic perfection. No doubt they succeeded in producing masterpieces. Michelangelo’s “Statue of David” and Leonardo da Vinci’s painting of “Mona Lisa” are just a couple of examples of such objects of ever-lasting beauty. Several works of the renowned painters Rembrandt and Raphael exude GR geometry.
It is said that in the modern day world also, several plastic surgeons employ the techniques of GR to give a better shape to faces. Make-up men in the film world too employ GR ideas to enhance the physical features of the stars.
Once again, let us turn to mathematics for a while. Italian mathematician Fibonacci propounded a special series of numbers, where each number is the sum of the two preceding numbers -- 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377,…….. The greatness of this sequence is that any number in the series divided by the previous number yields GR approximately!
Flower petals
Researchers have found to their immense amazement that Fibonacci number patterns occur in abundance everywhere in nature – flowers, leaves, plants, shells, animal world and even micro-organisms.
In the case of sunflower and pineapple fruit, adherence to the Fibonacci sequence is very exact. Let us look at the array of seeds in the centre of a sunflower. We will notice spiral patterns curving to the left and the right. The total of each of these two types of spirals will be a Fibonacci number! The scaly formations on the outer surface of a pineapple present a similar picture.
Researchers have found to their immense amazement that Fibonacci number patterns occur in abundance everywhere in nature – flowers, leaves, plants, shells, animal world and even micro-organisms.
If we count carefully the number of petals in a flower belonging to most of the known varieties, it is a Fibonacci series number! For example, lily has 3 petals and hibiscus 5 petals. Similarly we have single-petalled, double-petalled, 8-petalled, 13-petalled, 21-petalled, 34-petalled flowers and so on. This is the result of GR play in the plant world!
Seeds in a sunflower
In the case of sunflower and pineapple fruit, adherence to the Fibonacci sequence is very exact. Let us look at the array of seeds in the centre of a sunflower. We will notice spiral patterns curving to the left and the right. The total of each of these two types of spirals will be a Fibonacci number! The scaly formations on the outer surface of a pineapple present a similar picture.
In DNA too!
Further, tree branches and leaf arrangements around a stem have GR-based formations. Interestingly, human DNA molecules too exhibit the Fibonacci sequence in double-helix cycles. Snail shells, bee hives and host of other animal world creations display these features. Even snowflakes fall in line.
Let us now turn to some of the architectural marvels of the world – the Great Pyramid in Egypt, the temple of Parthenon in Greece and our own Taj Mahal. It is interesting to note that these edifices, constructed at widely different points of time in the history of mankind and in varying geographical locations, incorporate GR in them. Whether it is by accident or by design remains a matter of conjecture.
(To be continued)
