Welcome All… to the Montessori Learning Path.

Creativity and freedom .. these 2 words (aside from love and compassion) i believe, are 2 key words that describe part of the image of God that we were created in….

Q. So what does Fibonacci and the flower of life have to do with that?…

Ans: Read On…

I believe in nature the flower of life and the Fibonacci series describes ultimate creativity and freedom.

Q. So what has that got to do with school, education and kids.

Ans: Everything. it’s what we want them to excel in. You cannot have creativity without freedom.

The International school that i was a part of found themselves in a position to express this creativity when they needed a new Junior High School classroom.

However we were to use an old building and renovate or refurbish the upper level for the classroom.. so we did not have complete freedom.

The allocated space for the classroom must have high positive energy, and an aesthetic conducive for growing and learning. A safe place where creativity can be let loose without fear of criticism.. total freedom to express and grow.

Actually the students produced a wish list of approximately 100 items including a hangout area and a fireman’s pole for quick exit.

We had limited space so the design must use the space efficiently.. and not one but 2 classrooms needed to fit into the space.

Our architect had a plan to design the layout based on the Flower of Life and the Fibonacci series / sequence, both being good learning and energy aesthetics. The dividing wall, the mezzanine floor and window features could all reflect the curves and patterns of the flower of life and Fibonacci series.

Hey…. woahhh there… many readers may be getting lost by now. FIRST– What the heck is the Fibonacci series and the Flower of Life?

Okay good question.. and here is where the creativity and freedom of God’s design is shows up all over nature, Read on…

## The Fibonacci series

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…. can you continue it?

(pssssstt… here’s a tip: add the previous 2 figures to get the next number..)

A visual of the series looks like this: (above numbers are represented by square’s relative dimensions)

Now, for fun, take the ratio of two successive numbers, divide each by the number before it, and we find that the series of numbers that follow

settle down to a special number in mathematics..

1/1 = 1

2/1 = 2

3/2 = 1.5

5/3 = 1.6666…

8/5 = 1.6

13/8 = 1.625

21/13 = 1.61538…

34/21 = 1.61904…

As we progress down we see that The ratio gets nearer and nearer to a particular value, which we call the golden ratio (Phi=1.618).

Now if we take this golden ratio and use it as the growth factor for a logarithmic spiral (a golden spiral) we get a spiral very similar to the Fibonacci spiral above. Just saying.

Don’t worry the secret will reveal itself as we go on.

The Fibonacci sequence / series is seen in all aspect of life:

Let’s look at — BUNNIES & The Fibonacci Sequence:

Let’s say you have two rabbits male and female (for want of a better term we will call that a couple). In month 1 The rabbit couple are not mature enough to produce, but in month 2 and the ongoing months, they produce an offspring of new couple of rabbits every month. If all the new rabbit couples reproduce in the exact same way and none of the rabbits ever die, how many couples’ of rabbits will there be at the start of the first? The second? The third? The fifth month.. etc

After one month, there is still one couple, after two months there are 2 couples, then 3 couples, then 5 couples… is this starting to look familiar?

Fibonacci (the Italian mathematician) developed the sequence after examining the rabbit example above. Thus the sequence was attributed to his name.

A list of numbers must be mathematically related to become a ‘sequence’ or a series and as previously explained the sequence is gained by adding the previous to figures together to get the next number.

1, 1, 2, 3, 5, 8, 13…

1 + 1 = 2 ; 1+ 2 = 3; 2 + 3 = 5; 3 + 5 = 8; 5 + 8 = 13… What number comes next in the sequence?

Now come the fascinating part: The numbers in the Fibonacci Sequence appear in various forms in nature over and over and over again. Most of the time the initial part of the series, the smaller numbers, are apparent. But on occasions

there appears examples of the larger numbers. For example; It seems that nature utilises the numbers in the Fibonacci Sequence /series to create the most efficient and largest surface area to give the maximum exposure to sunlight allowing optimum growth of the plant.

Question: Why is it we see more often that the number of petals in a flower is one of the Fibonacci numbers: 3, 5, 8, 13, 21, 34 or 55?

For example, A lily has three petals, the buttercup has five, the chicory has 21, and the daisy very often has 34 or 55 petals, etc.

And again, when we examine the top of sunflowers, we see two series of curves, one curving in one way and the 2nd curving in another. The number of spirals not being equal in each of the ways.

Why is it that often the number of spirals is either 21 and 34, OR 34 and 55, OR 55 and 89, OR 89 and 144?

The same thing occurs in pine-cones : why is it that they have 8 spirals from one side and then 13 from the other side, OR 5 from one side and 8 from the other?

Also why is it that the number of diagonals of a pineapple is 8 in one direction and 13 in the other direction?

Are these numbers a result of chance? NoT AT ALL! They all belong to and are a part of the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. (where each number results from the sum of the two preceding numbers).

Many scientists and mathematicians have noticed for along time that these numbers seem to have some great importance in nature. But it is only fairly recently that we have come to understand the reason why. It seems to follow optimum growth process for a plant which creates a growth pattern which optimises the leaf area exposed to sunlight allowing the greatest possible nutrient intake for the plant.

As you have seen the Fibonacci sequence is linked to the golden mean which itself has been associated with the spirals of certain shells.

The correspondence of the Fibonacci numbers with the pineapple, the sunflower and the pinecone is shown to be very exact. However in the example of the flower petals it is only on average.

Did you know that a jelly fish creates a mirror image of itself when swimming through the water.

See drawing.

If you carefully examine further you can see the Golden ratio (Fibonacci curve) and the flower of life coming together.

SO… now you may be asking What the heck is the flower of life?

The Flower of Life is a geometrical figure which is made up from multiple overlapping circles, evenly spaced that are organised so that they produce a flower-like hexagon pattern with six fold symmetry.. see diagram

Anyway.. where were we? OHHHH yes, The junior High School

We want to design the plan layout around the flower of life and Fib. So we start by taking the centre point of the room plan and growing out the flower of life pattern from there.

Following this the partition wall and outline of the upper mezz floors were traced. See plan drawing.

Annnnnnd…. Voilaaa:

We now have a flower of life curved wall separating the 2 classrooms (by the way the wall has 8 skins and a 100mm air gap for sound proofing 🙂

We also have 2 small upper levels (Mezz floors) for chilling out, reflection / meditation etc.

All shapes following the flower of life. Even the storage locker area has the curves !!

By the way the actual number of lockers on each level were place in the Fib series. Total of 20 spaced as 1,1,2,3,5,8 = 20

And don’t foget the window accessories … recognise the shape in the photo?

We did not forget the students’ request of the “gotta-leave-the-building-quick” alternative exit — Fireman’s pole. This is definitely NOT curved.

FIB in a heart shape.

So let’s end with a challenge and an observation exercise:

As you go through our day, see how many patterns of Fib sequence and/or flower of life examples you can see. Make it a game with your friends.

Happy hunting,

God Bless