#Fibonacci sequence in nature examples series#

If you take two consecutive numbers in the Fibonacci Sequence and divide one number by the one that comes before it, then you get a number that will get closer and closer to ϕ.įor example, if we divide each number in the Fibonacci sequence by the previous number in the sequence,ġ, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …that gives us: 1 / 1 = 1, 2 / 1 = 2, 3 / 2 = 1.5, and so on up to 144 / 89 = 1.6179.

Today this number is mostly called 'phi' and is expressed in writing using the Greek symbol ϕ. The golden ratio is an irrational number approximately equal to 1.618. The golden ratio is a stunning mathematical extension of the Fibonacci sequence. How is the golden ratio related to the Fibonacci sequence? Mathematically, the Fibonacci sequence is represented by this formula Fn = Fn-1 + Fn-2, where n > 1.įibonacci’s famous book Liber Abaci compared the Hindu Arabic numeral system with other systems, such as Roman numerals, and described how using the Hindu Arabic system made calculations faster and easier. Individual numbers in the sequence are often referred to as Fibonacci numbers.

#Fibonacci sequence in nature examples series#

As you can see, every number in this series or sequence is obtained by adding the two preceding numbers. The sequence is derived by adding the two numbers before it, so if you start with zero, the next number will be one, followed by one, followed by two, three, and so on. The Fibonacci sequence is a recursive series of numbers where each value is determined by the two values immediately before it. They’ll soon discover that Fibonacci sequences are everywhere! Artists and architects have used it throughout history, from the Pyramids of Giza and Da Vinci's Mona Lisa to Twitter and Pepsi logos. Students can even find Fibonacci sequences on their own bodies! We have five fingers, and each finger is divided into three parts, all of which are Fibonacci numbers (including the lengths of the bones in our hands). You can also show students how the Fibonacci sequence is represented by the logarithmic spirals in the chamber of a nautilus shell. The numbers of seeds or leaves in these spirals are also generally in the Fibonacci sequence. Cacti leaves and sunflower seeds are arranged in both left and right-handed spirals. For example, if they've ever counted the number of petals on a fully intact flower, they'd have discovered that the number of petals is a Fibonacci number! Many flowers have 3, 5, 8, 13, or 21 petals, which are numbers from the Fibonacci sequence. Students will be amazed to learn the remarkable ways these concepts are found in their everyday life. In mathematics, the Golden Ratio (aka golden mean, or divine proportion) and the Fibonacci sequence are derived from his work. Fibonacci (aka Leonardo Bonacci, aka Leonardo of Pisa) was an Italian mathematician who introduced the Hindu-Arabic number system (0-9) in 1202 when Europeans still used Roman numerals.