Prof. Andrew Stapleton, at U. Wisconsin-La Crosse, provides another interesting exercise to liven up your OM class.
The Fibonacci sequence, introduced by mathematician Leonardo Fibonacci from Pisa, Italy in the 12th century, is a number sequence where each term is the sum of the preceding ones. A typical Fibonacci sequences looks like: 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. While this is the most well-known version, Fibonacci numbers can begin with any two numbers on the number line as long as they follow the same pattern of addition.
The sequence is closely related to the Golden Ratio, a concept that appears frequently in nature (e.g., in the spiral pattern of shells or of sunflowers) and art (e.g., proportions in Renaissance paintings).
Interestingly, the Fibonacci sequence also has practical applications in Operations and Supply Chain Management. It can be applied in areas such as supply chain network design, forecasting inventory fluctuations, resource allocation, and even in facility layout optimization.
Fun Math Trick using Fibonacci Sequence
Here is an engaging way to explore Fibonacci numbers with your students:
1. Have a student pick any two numbers, say 5 and 4.
2. Add the numbers together (5+4=9).
3. Now, take the second and third numbers (4+9=13)
4. Continue the process for ten steps and calculate the sum.
For example, start with 5 and 4. These yields: 5, 4, 9, 13, 22, 35, 57, 92, 149, 241.
Now calculate the sum of the sequence. The sum is 627.
How to Predict the Sum:
Before calculating, you can impress your students with a neat trick! Here’s how:
Instead of adding all of the numbers manually, look at the fourth number from the bottom of the list. In this case, it is 57.
Multiply the number by 11.
57 x 11 = 627 – this gives you the total sum without having to add them up.
This works because the Fibonacci sequences follow a predictable pattern:
This is what the list of numbers will be:
a
b
a + b
a + 2b
2a + 3b
3a + 5b
5a + 8b
8a + 13b
13a + 21b
21a + 34b
The sum is 55a + 88b, which is 11 times the seventh number. Since multiplying by 11 is a relatively simple calculation, this creates a fun and useful math trick to amaze your students and connect math concepts to OM.