Leonardo Fibonacci was an Italian mathematician who lived from 1170 to 1240. While Fibonacci was growing up, he was sent to study mathematics with an Arab master. Once he finished studying, he began to travel to other countries to study their mathematics and calculations (Encyclopedia Britannica). In 1202, Fibonacci published his book that was entitled Liber Abaci or Book of the Counting. In this book, he used Hindu-Arabic numbers. This is the number system that we are using today. Prior to his writing, many people did not know or use this system of numbers. In the beginning, Fibonacci talked about how this system worked, basically how to use, write, and compute with these numbers. He taught this by focusing on real life examples…show more content… The formula used is F_n= F_(n-2)+F_(n-1). In order to calculate the nth term another formula, known as Binet’s formula, is used. It states F_n=(φ-(-φ)^(-n))/√5 where φ=(1+√5)/2≈1.61803. The Fibonacci sequence has led to many mathematical advances over time, and it is used in many different areas of life. It is an important part of life due to its ever present appearances throughout nature, mathematics, pop culture, and business. The Fibonacci Sequence is most important in the world of mathematics. It is found in other discoveries like Pascal’s triangle and Cassini identities.
One area of mathematics that overlaps with the Fibonacci Sequence is the Golden Ratio which is typically used when discussing the ratio of distances (wolfram alpha). The ratio is approximately 1.6180. It is found by this formula φ= (1+√5)/2≈1.61803 . The ratio has been surrounded by mystery since the time of the ancient Greeks. Many scholars look at the Parthenon statues (built by Phidias, from 490-430 BC) and believe that they were built using the Golden Ratio. Euclid, during his lifetime, became the first to define this ratio. He defined it as “extreme and mean ratio” (Wikipedia). Credit is generally given to Phidias hence the symbol phi is used when denoting the ratio (UIUC). The Golden Ratio is similar to the ratio between each consecutive Fibonacci number.
Fibonacci numbers also overlap with Pascal’s Triangle, which is found on the right. The triangle is formed by adding the