The true universal numbers
By Chitwan Khosla, Features Editor
Numbers are fascinating. Be it the constants in numerous laws of physics, the arrangement of electrons in an atom, the value of pi in math, or the Pythagorean theorem, numbers have played a key role in making complicated phenomena easier to understand and establish.
Technological advancement and scientific developments owe a lot to numbers, but numbers are also critical in exploring the marvels of nature. Have you ever wondered why there are exactly the same number of petals in a lily flower and why they’re in a definite pattern? Have you ever pondered why a species of fish has the same pattern of fins? Or why all humans have a specific number of bones? All these questions are again answered by numbers. These numbers are called Fibonacci numbers. Often referred as nature’s numbering system, the Fibonacci numbers are a sequence of numbers which have a linear arithmetic progression pattern.
The basic series of Fibonacci numbers is 1, 1, 2, 3, 5, 8, 13, and so on. Some start the series from zero, but the pattern is definite: the next number is the sum of the previous two. Hence, the next number of the series should be 21 (8 + 13). The set of numbers are fixed, and almost every known arrangement in nature follows this pattern.
Interestingly, we also observe a spiral pattern in nature which is formed by connecting the squares with widths from Fibonacci numbers in an anti-clockwise fashion. This is called the golden spiral. If we divide anything the squares or rectangles of the width of Fibonacci numbers, we would have a pattern of golden rectangles. This is what we get to see in far-off galaxies and in hurricanes on the surface of Earth. We also witness the golden ratio which is a fixed number (1.618034 approx.). The ratio of any two consecutive Fibonacci numbers is equal to or approximately equal to the golden ratio. This ratio has supposedly been used in construction of the Pyramids of Giza as well as by Leonardo Da Vinci.
Although various evidence shows that Fibonacci numbers were discovered and understood in ancient India, the modern world came to know about these in the 1200s from Leonardo Bonacci (Fibonacci), a famed Italian mathematician. With his book, Liber Abaci, Bonacci introduced the world to the Hindu-Arabic numbering system and the Fibonacci numbers. He used the example of a pair of rabbits. Assuming that newly born male and female rabbits are kept together and that the rabbits are capable of breeding once they are one month old, how many rabbits would be there in the population at the end of the first year. On solving the puzzle, the solution was: one pair at the end of the first month, two pairs at the end of the second, three pairs at the end of the third, and then five pairs at the end of the fourth. The progression is now in the pattern of the Fibonacci numbers (1, 2, 3, 5, 8…).
The universe around is full of Fibonacci and golden ratio arrangements. The shell of a snail is in the pattern of a golden spiral. The centres of flowers show the spread of seeds in the progression of golden spirals. The arrangement of branching of trees and stems, even the roots of the plants grow in the pattern of Fibonacci numbers. Apart from these examples, Fibonacci numbers are also a major part of music and other forms of art that we hear or see. Da Vinci’s Mona Lisa is a famous example. It can be divided into the golden rectangles starting from the lady’s nose going in the clockwise manner.
The GoldenNumber.net explains how music has roots in Fibonacci numbers. Many specialists and mathematicians believe that Mozart was aware of the importance of Fibonacci numbers in music. A single note has 13 notes in its span through its octave, and a scale is composed of eight notes. The fifth and the third notes are foundations of all the chords and are based a combinational tune of two steps and one step from the root tone which in turn is again the first note of the scale.
No matter if we believe in the logical reasoning of the Fibonacci numbers or we consider all this as a mere coincidence and an imaginative view of things, one thing is pretty evident: these numbers and patterns are truly magical!