Fibonacci, Flower of Life & Junior High School - Sunrise

Q: What has Fibonacci and The Flower of Life got to do with the Junior High School...
Ans: Read On...

The whole space for the JHS should be an environment with good positive energy and a vibe conducive for learning and growing. A place where creative thinking can foster and grow.  A space that gives a feeling of being connected, of being safe and secure. Students also hoped it would include a hangout area too.

Efficient use of space is a must if 2 classrooms are to be made in the limited space allotted.

Heinz, our architect, designed the plan area based on the Flower of Life and the Fibonacci sequence. A design conducive for good learning and energy aesthetics. Partition wall, mezz floor and window decor could all include the flower of life “curves”

Hey but hold on a moment -- What is the Fibonacci series? and Flower of Life?

Here is a 'Fibonacci series':

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

(pssstt... just add the previous 2 figures to get the next number..)

OR Visually (the numbers are now the lengths of the sides of the
squares... ) :

                                                                                         

Now, If you take the ratio of two successive numbers in the series and divide each by the number before it, we will find the following series of numbers.

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...

The ratio seems to be settling down and getting nearer and nearer to a particular value, which we call the golden ratio(Phi=1.618..)...

A golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. In practical terms, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes. Interestingly this spiral approximates the Fibonacci spiral.

BUNNIES and The Fibonacci Sequence
The Fibonacci sequence appears in all areas of life: 

Suppose you own a pair of rabbits. These rabbits are too young to produce at one month, but beginning in their second month they produce a new pair of rabbits every month. If all the new rabbit pairs reproduce in the same way and none ever die, how many pairs of rabbits will there be at the beginning of the first month? The second? The third? The fifth? 

After one month, there is still one pair, after two months there are 2 pairs, then 3 pairs, then 5 pairs... Look familiar?

By examining the rabbits, Fibonacci developed the sequence now having his name.

In order to be considered a mathematical sequence, a list of numbers must be somehow mathematically related. What is the relationship between the numbers in the Fibonacci Sequence?

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?

The numbers in the Fibonacci Sequence appear again and again in various forms in nature. Most often the smaller numbers appear, but occasionally examples of larger numbers do appear. It is believed that nature uses the numbers in the Fibonacci Sequence in order to create the greatest surface area to permit sunlight and nutrients, however, no concrete evidence exists for this 

perception

                 

        

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

For example, the lily has three petals, buttercups have five, the chicory has 21, the daisy has often 34 or 55 petals, etc.

Furthermore, when we observe the heads of sunflowers, we notices two series of curves, one winding in one way and one in another; the number of spirals not being the same in each way. 

Why is the number of spirals in general either 21 and 34, either 34 and 55, either 55 and 89, or 89 and 144? 

The same for pine-cones : why do they have either 8 spirals from one side and 13 from the other, or either 5 spirals from one side and 8 from the other? 

Finally, why is the number of diagonals of a pineapple also 8 in one direction and 13 in the other?

Are these numbers the product of chance? No! They all belong to the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. (where each number is obtained from the sum of the two preceding). 

A more abstract way of putting it is that the Fibonacci numbers f_n are given by the formula f₁ = 1, f₂ = 2, f₃ = 3, f₄ = 5 and generally f _n+2 = f_n+1 + f_n . 

For a long time, it had been noticed that these numbers were important in nature, but only relatively recently that we understand why. It is a question of efficiency during the growth process of plants. Creating a growth pattern allowing the maximum leaf area to be exposed to sunlight for optimum nutrition intake for the plant.

The Fibonacci explanation is linked to another famous number, the golden mean, itself intimately linked to the spiral form of certain types of shell. Also in the case of the sunflower, the pineapple and of the pine-cone, the correspondence with the Fibonacci numbers is very exact, while in the case of the number of flower petals, it is only verified on average (and in certain cases, the number is doubled since the petals are arranged on two levels).

When jelly fish swim through water they create a mirror image of themselves.
This drawing shows the mirroring effect. Studying it further one can see how
the flower of life and the golden ratio (Fibonacci curve) nest together.

SO…What is the flower of life?

The Flower of Life is the modern name given to a geometrical figure composed of multiple evenly-spaced, overlapping circles, that are arranged so that they forma flower-like pattern with six fold symmetry like a hexagon - see opposite

So let’s get back to the junior High School

The plan drawing of the room was taken and the central point was used to start the
flower of life pattern. From this the dividing wall and mezzanine floor shapes were drawn. Note the flower of life curves being followed in the plan design.

   So now we have 2 classrooms separated with a curved wall..

… but not ANY curve right?

Then we have 2 small upper floors (mezz) for hangout, contemplation and chilling-out.

Again the shape of the floors boundaries are curved….. but not just ANY  curve right?

Then we have the storage lockers. Again curved as in the flower of life and the lockers 

placed in the Fibonacci sequence. 1,1,2,3,5,8 = 20


     




                                                                         

 The Fibonacci sequence is also demonstrated in the the window decor....                                                              

Then we have the quick … “I gotta go to the loo fast” alternative building exit,

Fireman’s pole which is straight and NOT curved, right?  

The Heart Shaped Fib.






Now It's your turn.
Your Challenge:

Note down how many examples of the Fibonacci sequence and the Flower of Life patterns you can spot in a day... make the challenge with your friends, parents and siblings.. GO!!

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