Real Mathematics: Pattern #4

Leonardo Pisano

Italian town Pisa was the home of an ingenious person named Leonardo Pisano, which means Leonardo from Pisa. He was not only essential to history of mathematics, but he was also influential for the birth of scientific revolution. It is not a surprised that Leonardo Pisano was from Italy as Italians were involved with Arabs through trading.

Arabs knew an amazing way of counting and calculating, which were done with a system called decimal system. I’ll talk about that story in another article.

Leonardo Pisano was the first known person who brought modern numbers Western Europe. Although this was an amazing accomplishment, his importance comes even more fascinating if you look at what he did for patterns.

The Rabbit Problem

If I wrote his name as Fibonacci, then majority of you would understand what problem I’ll mention in the following:

In a farm, there is one couple of baby rabbits. A rabbit couple can give birth to baby rabbits only after their 2nd month and they can continue giving birth each month after that. Leonardo Pisano tried to find out the number of rabbit couples after one year.

Solution

First month there is a baby couple. This couple will be adult in the second month and they will give birth to one couple baby rabbits in the third month.

In the fourth month first couple reproduces as the second couple becomes an adult.

IMG_5681

In the fifth month first and second couples have new babies as third couple becomes an adult.

IMG_5682

In the sixth month first, second and third couples have new babies as the fourth and fifth couples become an adult.

IMG_5683

IMG_5690At this point we can point out a pattern in the number of rabbit couples. After second month, total of previous two months gives the number of rabbits in the next month. For example number of rabbit couples in the third month becomes the summation of first and second months, which is 1+1=2.

Fourth month = Second month + Third month = 1 + 2 = 3… and so on.

 

Then number of rabbit couples after one year (twelve months) is:

IMG_5694

Beauty of Fibonacci

This number sequence is known as the Fibonacci sequence and it is visible to us in nature on so many occasions. I’ll be talking about the most popular examples of Fibonacci sequence in the following articles.

Real life examples of math subjects are crucial, especially the ones from nature itself. But most of the population lives in the cities and this force us math teachers to find out examples from modern life.

Stairs and Fibonacci

Imagine that you have to climb up from stairs inside your apartment.

  1. How many ways are there to climb 3 steps?
  2. How many ways are there for 5 steps, 6 steps, 8 steps and n steps?
  3. What is the relationship of this question and Fibonacci numbers?

M. Serkan Kalaycıoğlu

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