The first ten numbers of the famous Fibonacci sequence are
1 1 2 3 5 8 13 21 34 55 89
Can you spot how the sequence flows?
To get the next number in the sequence you add together the previous two. As two numbers are needed to get the Fibonacci sequence started, 1 and 1 are used in this case. The sequence is named after Leonardo da Pisa (who was also called Fibonacci) a 12th century Italian merchant who came up with the sequence when trying to find a way of modelling the population of rabbits!
Mathematicians are fascinated by the Fibonacci series because it occurs in so many different places in nature. It is common for the number of petals found on a flower to be a Fibonacci number, the way sunflower seeds and pine cones follow a spiral pattern also follow the sequence.
In fact, Fibonacci numbers can be found anywhere. Just think of a piano keyboard-an octave on a keyboard is made up of 8 white keys and 5 black keys. The black keys are positioned in a group of 2 and a group of 3. In total there are 13 keys in one octave-all Fibonacci numbers!
Puzzle 1
Calculate the next ten Fibonacci numbers, starting with 89 as above.
Puzzle 2
Calculate the ratios of successive Fibonacci numbers. To do this, divide each number by the next number in the sequence (e.g. 1/2, 2/3, 3/5 etc). Do this for the first 20 numbers. What do you notice about the answer?
Perhaps even more special is what happens when you take the ratios of successive Fibonacci numbers- 1/2, 2/3, 3/5, 5/8, 8/13 etc. The answer gets closer and closer to the Golden Ratio (R) which is approximately 0.61803.
The Golden Ratio (R) is a very special number and has been used since Ancient Greek times. Paintings that have a height to width ratio that equals the Golden Ratio are more pleasing to the eye. Many buildings also incorporate the Golden Ratio in their design.
The Golden Ratio is important in architecture and even in five-pointed stars (for example, the stars on the European flag are made by cutting the diagonals of a pentagon according to the Golden Ratio). In fact, even our bodies follow the Golden Ratio, from the proportions of our whole body to those of our heads, face and hands!
