There are over 30,000 species of bees and in most of them the bees live solitary lives. The one most of us know best is the honeybee and it, unusually, lives in a colony called a hive and they have an unusual Family Tree. In fact, there are many unusual features of honeybees and in this section we will show how the Fibonacci numbers count a honeybee's ancestors (in this section a "bee" will mean a "honeybee"). First, some unusual facts about honeybees such as: not all of them have two parents!
In a colony of honeybees there is one special female called the queen.
There are many worker bees who are female too but unlike the queen bee, they produce no eggs.
There are some drone bees who are male and do no work. Males are produced by the queen's unfertilised eggs, so male bees only have a mother but no father!
All the females are produced when the queen has mated with a male and so have two parents. Females usually end up as worker bees but some are fed with a special substance called royal jelly which makes them grow into queens ready to go off to start a new colony when the bees form a swarm and leave their home (a hive) in search of a place to build a new nest.
So female bees have 2 parents, a male and a female whereas male bees have just one parent, a female.
Here we follow the convention of Family Trees that parents appear above their children, so the latest generations are at the bottom and the higher up we go, the older people are. Such trees show all the ancestors (predecessors, forebears, antecedents) of the person at the bottom of the diagram. We would get quite a different tree if we listed all the descendants (progeny, offspring) of a person as we did in the rabbit problem, where we showed all the descendants of the original pair.
Queens have 2 parents
Males have 1 parent
Let's look at the family tree of a male drone bee.
2. He has 2 grand-parents, since his mother had two parents, a male and a female.
3. He has 3 great-grand-parents: his grand-mother had two parents but his grand-father had only one.
4. How many great-great-grand parents did he have?
Again we see the Fibonacci numbers :
Number of of a MALE bee:
of a FEMALE bee: 2
grandparents 2 3
great-grandparents: 3 5
great,great grand parents: 5 8
gt,gt,gt grand parents: 8 13
The Fibonacci Sequence as it appears in Nature by S.L.Basin in Fibonacci Quarterly, vol 1 (1963), pages 53 - 57.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ..More..
1. Make a diagram of your own family tree. Ask your parents and grandparents and older relatives as each will be able to tell you about particular parts of your family tree that other's didn't know. It can be quite fun trying to see how far back you can go. If you have them put old photographs of relatives on a big chart of your Tree (or use photocopies of the photographs if your relatives want to keep the originals). If you like, include the year and place of birth and death and also the dates of any marriages.
2. A brother or sister is the name for someone who has the same two parents as yourself. What is a half-brother and half-sister? Describe a cousin but use simpler words such as brother, sister, parent, child?
Do the same for nephew and niece. What is a second cousin? What do we mean by a bother-in-law, sister-in-law, mother-in-law, etc? Grand- and great- refer to relatives or your parents. Thus a grandfather is a father of a parent of yours and great-aunt or grand-aunt is the name given to an aunt of your parent's.
Make a diagram of Family Tree Names so that "Me" is at the bottom and "Mum" and "Dad" are above you. Mark in "brother", "sister", "uncle", "nephew" and as many other names of (kinds of) relatives that you know. It doesn't matter if you have no brothers or sisters or nephews as the diagram is meant to show the relationships and their names.
[If you have a friend who speaks a foreign language, ask them what words they use for these relationships.]
3. What is the name for the wife of a parent's brother?
Do you use a different name for the sister of your parent's? In law these two are sometimes distinguished because one is a blood relative of yours and the other is not, just a relative through marriage.
Which do you think is the blood relative and which the relation because of marriage?
4. How many parents does everyone have?
So how many grand-parents will you have to make spaces for in your Family tree?
Each of them also had two parents so how many great-grand-parents of yours will there be in your Tree?
..and how many great-great-grandparents?
What is the pattern in this series of numbers?
If you go back one generation to your parents, and two to your grand-parents, how many entries will there be 5 generations ago in your Tree? and how many 10 generations ago?
The Family Tree of humans involves a different sequence to the Fibonacci Numbers. What is this sequence called?
5. © Looking at your answers to the previous question, your friend Dee Duckshun says to you:
o You have 2 parents.
o They each have two parents, so that's 4 grandparents you've got. o They also had two parents each making 8 great-grandparents in total ... o ... and 16 great-great-grand-parents ... o ... and so on.
o So the farther back you go in your Family Tree the more people there are. o It is the same for the Family Tree of everyone alive in the world today. o It shows that the farther back in time we go, the more people there must have been. o So it is a logical deduction that the population of the world must be getting smaller and smaller as time goes on!
Is there an error in Dee's argument? If so, what is it? Ask your maths teacher or a parent if you are not sure of the answer!
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ..More.. E
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