“Fibonacci? Isn’t that a pasta?”

I rolled my eyes at my friend. “No,” I replied, “it’s got to do with maths.” He gave me a funny look and said “But you hate maths!” I nodded in solemn agreement “I know.”

And I do hate maths. I have hated it since grade 3 when I can distinctly remembering my teacher making me stay in at lunch to finish some problem I was stuck on. I can remember fuming and becoming more and more upset as I desperately tried to get the problem. What I learnt instead? Maths sucks, and I never want to do it again.

This has been a pretty good theme throughout my life, and I have somewhat successfully avoided it. But when I heard there was a sequence called Fibonacci that helps to describe how bees reproduce, I had to investigate.

But before I get into my wonderful bees, let me start with immortal rabbits. The idea that Leonardo Fibonacci in 1202AD had was that if you had a breeding pair of rabbits that never died, then the population would grow like this: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… (you get the idea). In this sequence each number is the sum of the proceeding two numbers.

Fig. 1 Thank goodness rabbits aren’t immortal, even if they are really cute.

These numbers also have lots of really amazing properties. I’ll only list 2 here, but there are lots more.

• Choose any 3 adjacent numbers and square the middle. Then multiply the first and third. The difference between the two will always be 1.
• This time, take any 4 adjacent numbers and multiply the first and last, and multiply the middle. The result of the first and last multiplication will always be only one more or one less than the middle multiplication.

Fig. 2 A blue banded bee (Amegilla cingulata), my favourite.

But what has this sequence got to do with bees? Well female bees can reproduce with or without a male. Unfertilised females can only produce males (drones), but fertilised they can produce females (workers) as well (they can choose what sex to produce depending on the numbers in the hive).

So if you take 1 drone and trace its ancestry, it will look something like this:

Do those numbers look familiar? (If they don’t look back to the immortal rabbits)
Just another reason why bees (and sometimes maths) are great.

References:

1. Simanek, D. “Fibonacci Flim-Flam”. LHUP.
2. The Fibonacci Numbers and the Ancestry of Bees, American.
3. Adam, J.A. (2003) Mathematics in Nature. Princeton University Press, New Jersey.

Figures – Licensed under Creative Commons

3 Responses to ““Fibonacci? Isn’t that a pasta?””

1. katied says:

Loved this post! Your blog post combined the two things I love most: adorable animals & maths. Good job! 🙂

2. Lucy says:

Hey thanks for the reply. Your piece is also really interesting! Makes you think what else can maths explain.

3. akamsteeg says:

Fibonacci strikes again!! It’s so incredibly interesting that bees reproduction fit the Fibonacci sequence! That man sure was a genius. I love maths, and I seriously love finding patterns in nature that express this sequence — such as the golden ratio!!! Great piece!