Saturday,  June 30, 2001
M I N D  G A M E S


The wonder of all wonders

"LOVE justice, ye rulers of the Earth!" reads the carving on a tenth century stone at the entrance of this Italian town where one of the seven wonders of the world stands, rather leans. At midnight, a car stops at the Leaning Tower end of the cemetery next to the cathedral of Pisa. Four men step out of this car and stop before a forgotten statue that citizens of Pisa installed 800 years ago. The torch-light beam rests on the face of the statue and, for the first time in 30 years, a smile crosses the intruder's lips. "Dig, dig!" he says to his men as he points towards the ground near the base of the statue. The men dig out an iron box from the spot, which contains a book written on gold plates. At the sight of gold, greed takes over the diggers and they draw weapons on the man who brought them here.

"Thanks for leading us to the treasure, we take over from here," they say. "Take the gold. That's not the treasure I want. I came here for the words written on the plates which are the guide to a bigger treasure," says the man. "Then, tell us what it says," the diggers say. "The words are of mathematician Leonardo Pisano 'Fibonacci' (pronounced Fib-on-archee) or Leonardo of Pisa, under whose statue we stand. Fibonacci says that he knows how God works. Look, here! He wants us to follow these instructions," says the man.

 


He reads out from the book as the diggers draw: "Begin with two adjacent small squares of size 1. On top of these, draw a square of size 2 (which is 1+1). Continue adding squares around the picture, with each new square having a side which is the sum of the sides of the latest two squares. Such set of rectangles are called the Fibonacci rectangles. The rectangles increase in size by a factor of phi (1.618034 or 0.618034 approximately, which is also called the golden mean) in a quarter of a turn. We can draw a spiral by putting together quarter circles, one in each new square. This is the Fibonacci spiral, a pattern similar to the shape of a sea shell. In Fibonacci series, beginning from one, every successive number is the sum of the previous two numbers."

"God has used this series in making everything. You have two hands, each of which has 5 fingers, each of which has 3 parts separated by two knuckles. The ratio of the length of the longest finger bone to the length of the middle finger bone is phi, which is also the ratio of the length of the middle finger bone to the length of the smallest finger bone, in every finger. The arrangements of leaves is the pattern for seeds and petals. The pattern in all is 0.618034... leaves, seeds or petals, respectively, per turn. In terms of degrees, this is 0.168034 of 360°, which is 222.492...°. If we see the smaller angle, it is (1-0.618034)*360 =0.381966*360 =137.50776°. If there are phi (1.618...) leaves per turn or phi (0.618...) turns per leaf, each leaf gets the maximum exposure to light, casting the least shadow on others." "God's a mathematician, and Fibonacci knew his secret! Good God!" say the diggers.

"Does the book tell why the Tower of Pisa leans?" they ask the man. "There's only one way to find out," says the man and takes out an equipment to measure the tower’s inclination to the vertical. "It is 16.1° — digits of the golden mean; the ghost of Fibonacci is pulling the tower," says the man and vanishes into the statue. His work is over; he has passed on the secret knowledge to the diggers.

— Aditya Rishi