Today's Beautiful Gem: `Musings on Phi' by M.
"Storm clouds caused by the spinning hurricane,
Waves in the ocean leaping to reach the moon,
Shells on the white sands of the endless shore,
Galaxies that spiral in the depths of space,
Sun-flowers that make the hearts beat faster,
Numerous pinecones that dot the trails of woods,
The music that is verily a treat to the ears,
Some architectural marvels that are a feast to the eyes,
Some paintings that stir the depths of the souls,
The virus that spreads disease and death,
The soccer ball that children kick around tirelessly,
The horns that adorn the animals' crowns,
The arrangement of the hexagonal hives of the bees,
And many more objects of great beauty in nature--
They all follow a sequence due to Fibanocci.
Logarithmic spirals are curves of life;
Golden ratios are personifications of beauty;
Pentagons and icosahedra are not harbingers of evil;
All items seemingly unrelated are related
By the one great irrational number phi,
Whose cousins are pi, e and so many others;
But Phi, it is the basis of arts and sciences;
Think of Phi and dream of Venus, the Love Godess!
No doubt, Phi is the spring of Life and Love eternal!"
Note: The integers 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... form
the Fibonacci sequence [f(n+1) = f(n-1) + f(n)]. f(100) is
354224848179261937664. The ratio of successive numbers [f(n) / f(n-1)]
in the limit is phi, the golden section number. Phi = 1.6180339887...
Index cards are 3"X5" or 5"X8" or a rectangular room is 21'X13' because
the effect is of such dimensions is pleasing. All the things
mentioned in the poem are related to phi in one way or other. As an
exercise, readers may try to prove to themselves that the reciprocal
of f(11) = 89 is a repeating decimal with a periodicity of 44 and may
be obtained by adding successively the Fibonacci numbers.
Om s'aantih: Peace! - J. K. Mohana Rao