Number Fun: The Fibonacci Sequence
Have you ever heard of the Fibonacci sequence? It is a series of unending numbers where each number is equal to the sum of the two before it. For example, the sequence includes: 0, 1, 1, 2, 3, 5, 8 and so forth. This can continue on forever. You may hear the term “the Golden Number” or the “Golden Ratio” associated with the Fibonacci sequence, and this refers to the ratio between the Fibonacci numbers . When you divide any number in the sequence by the number right before it the ratio approximates phi (1.618). The Egyptians used the Golden Ratio to build the pyramids while the Greeks used it to build the Parthenon. The Fibonacci numbers can be used in many different areas such as nature, astronomy, botany, computer science and even psychology. One example of the Fibonacci numbers in nature is that the number of petals on many plants is a Fibonacci number. Buttercups tend to have five petals, lilies tend to have three petals and asters tend to have 21 petals. Another example of Fibonacci numbers in nature can be found by looking at a pine cone. When you look at the object you will be able to clearly see Fibonacci spirals going around the cone. Every pine cone grows in spirals beginning where the stalk was attached to its base.
The Fibonacci sequence was discovered by a man named Leonardo Pisano Bigollo, whom people now refer to as Fibonacci. He was in his twenties and came from Pisa, Italy when he made the huge discovery. He decided to travel through the Middle East in the year 1202. During his journey he became fascinated with mathematical ideas from India that had spread west to Arabic countries. Upon his return to Pisa he published a mathematics book called “Liber Abaci” which featured these ideas from India. The book was considered a landmark in Europe. He asked a very important question in his book which referred to the Fibonacci sequence. His question began by stating that you have one pair (two) rabbits in an enclosed area. He wondered how many rabbits would be born if each month a pair of rabbits produced another pair of rabbits. The rabbits would begin giving birth two months after their birth. The answer to this question is the Fibonacci sequence. The Fibonacci sequence, in geometry, can be defined by: F(0)=0, F(1)=1, F(n + 2)=F(n) + F(n + 1) for every n > 0. The Fibonacci sequence is a discovery of great importance and can be used in many different ways in a variety of subject areas.
The following links all feature the Fibonacci sequence or numbers in some manner. The links include activity ideas, history and even lesson plans featuring the numbers