Of course we can but it isn’t wholly straightforward. Often in maths we don’t have to start from scratch (excuse the pun) we can actually go back 800 years to a similar problem posed by Leonardo of Pisa. In his Liber Abaci (Book of Calculations) he posed the following problem:
Suppose you have a male and female rabbit living in a field. How many rabbits will there be after 1 year?
The answer is “we can’t know”. But we can make an estimate making certain assumptions using maths which can give us a good guide to what might happen in the real world.
Leonardo tells us to make the following assumptions:
- The two rabbits are babies at the start
- No rabbits are eaten by predators. (They all live and stay in the field).
- Each female reproduces every month. A baby rabbit is ready to mate after one month.
- Each time a rabbit reproduces she gives birth to two baby rabbits (one male and one female)
As only female rabbits bear the young, we don’t need to consider the males (sorry) in our calculations. We could add the males in at the end. Another way to look at this is to consider the rabbits as pairs (1 male + 1 female). This was Leonardo’s approach and we will follow that. It is usually useful in problem solving to draw a picture.
Now, we could go on to 12 months. Not with pictures because there will be too many rabbits, we will do a table, another good approach in problem solving.
Now you may notice a pattern in the numbers in the table. Perhaps you even noticed the pattern in the drawing. At each month the total number of pairs is the sum of the totals for the previous two months.
1 + 1 = 2; 2+ 1 = 3; 3+2 = 5; 5+3 = 8; and so on.
Now that we see the pattern we can extend the series on without drawing a table:
1,1,2,3,5,8,13,21,34,55,89,144,233, 377, 610, 987, 1597, 2584,…..
The twelfth term in the series is 144. That is how many pairs of rabbits will be in the field at month 12. (although it could be interpreted as 233 at the start of the next year)
You may have seen this series before it is called the Fibonacci Series and comes up in the most surprising places in maths. Leonardo of Pisa is better known by his nickname “Fibonacci”.
This is a mathematical model that can help us predict what will happen in the future. Even if the mathematical equations are good and tested well, the outputs from such a model should be carefully interpreted. For instance, the Fibonacci model makes a lot of assumptions that may not reflect the real world. That is why mathematical models must be used with good science. Such models are often tested against real world data to see if they are useful. Usually they will be added to and modified as more knowledge becomes available.