Luke Hamilton's Grade 10 Personal Project at Bali International School - Fibonacci Blocks

1. Fibonacci
Blocks
Candidate Name: Luke Thomas Hamilton
Candidate Code: 001529-463
School Name: Bali International School
Date: 2nd February 2015
Supervisor: Matt McCormick
Luke Hamilton, Personal Project 2015

2. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Project Summary
The goal of my personal project is to create a
simple and fun educational tool to give people
an appreciation of the Golden Ratio and the
beauty they can create with it.
To achieve this, I have created a set of wooden
building blocks I’ve called:
Fibonacci Blocks.
Fibonacci Blocks are the first set of building blocks
based on the Fibonacci Sequence, Phi and the
Golden Ratio. When you play with the blocks, you
are following in the footsteps of Leonardo Da Vinci
by creating using nature’s golden proportions in
your creations.
Luke Hamilton, Personal Project 2015

3. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
My Topic
The topic of my personal project originated
from my passion for Maths and Sciences.
My Global Context is
Scientific and Technical Innovation
My project is an inquiry into how artists and
scientists have used the Golden Ratio to connect
the natural world with our human world and sense
of beauty. My product, the Fibonacci Blocks,
allows you to experience and appreciate this
connection for yourself.
Luke Hamilton, Personal Project 2015

4. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Investigating
I focused my research on five main areas:
1. Golden Ratio in Nature
2. Golden Ratio in Architecture
3. Golden Ratio in Art
4. The Fibonacci Series
5. The Froebel Blocks
My research in the first three areas allowed me to
improve from an outside interest in the Golden
Ratio to a in-depth understanding of it.
The last two became areas of inquiry that led me
to my product, the Fibonacci Blocks.
Luke Hamilton, Personal Project 2015

5. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Golden Ratio in
Nature
Fibonacci numbers and the golden ratio are
found throughout nature.
This includes in the spiral of sunflowers,
pineapples, shells and pinecones.
The more you are conscious of your
surroundings the more examples of the Golden
Spiral you will begin to notice.
It is also found in the human body, with the
proportion of the face, and the proportion of
our arms to our hands to our fingers, all
following the golden ratio.
Luke Hamilton, Personal Project 2015

6. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Golden Ratio in
Architecture
The Golden Proportion (also known as the
Divine Proportion) is the proportion used in the
design of famous buildings, from the Great
Pyramid in Egypt to the Taj Mahal in India to
the Parthenon in Greece to the Notre Dame
Cathedral in France.
Leonardo Da Vinci illustrated a Renaissance
Book written by Luca Pacioli called "De Divina
Proportione" (the Divine Proportion).
The book explained how, by using the Golden
Proportion, we could follow the proportions of
nature. It became an important book in the
design of art and architecture in the
Renaissance.
Luke Hamilton, Personal Project 2015

7. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Golden Ratio in
Art
Many Renaissance Artists used the Golden
Ratio in their art. Leonardo Da Vinci used it in
the proportions of “The Mona Lisa” and “The
Last Supper”. Michelangelo used it when
painting “The Creation of Adam” on the Sistine
Chapel Ceiling. Bottocelli used it in “The Birth
of Venus.”
The Golden Ratio is used
today in many different modern
designs. Here is an example of
this: The Apple logo, using
circles with the fibonacci
numbers 1,2,3,5,8,13.
Luke Hamilton, Personal Project 2015

8. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Fibonacci
Fibonacci, also known as Leonardo of Pisa,
was an Italian mathematician who introduced
the Hindu-Arabic numeral system to the West.
He also introduced the sequence called the
Fibonacci Series, where each number is the sum
of the two numbers before it, creating:
1, 1, 2, 3, 5, 8, 13 ,21, 34, 55, 89, 144 etc
He showed that when you divided each number
with the one before it in the sequence, each
number got closer and closer to the number
PHI, which has been known through history as
the “Golden Ratio”.
Luke Hamilton, Personal Project 2015

9. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Froebel Blocks
Friedrich Froebel was the creator of the
Kindergarten. He was the teacher to preschool
pioneers Rudolph Steiner and Maria
Montessori. To help teach young children, he
created "Froebel Blocks". These were wooden
blocks which allowed children to learn to think
in three dimensions.
Famous people who learned with Froebel Blocks
include Albert Einstein, Buckminster Fuller, Frank
Lloyd Wright & Charles Eames, and famous cubist
artists Paul Klee & Josef Albers.
It is the idea of the Froebel Blocks that inspired
me to create the Fibonacci Blocks - the first
blocks to be created using the Fibonacci Series
and Golden Ratio.
Luke Hamilton, Personal Project 2015

10. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
My Criteria
Inspired by the Froebel blocks, I set the criteria
for my Fibonacci Blocks.
The final criteria I set for my product were:
1. Be as easy and fun to use for students and adults
2. Capture the imagination of people who used them
3. Allow people to understand the Golden Ratio
4. Result in people using the blocks naturally
5. Be in exact measurements of the Fibonacci Series
6. Be good quality and long lasting materials
7. Be practical to carry and easy to pack and unpack
8. Be accompanied by an easy to understand,
educational and fun to read guide of good quality
Luke Hamilton, Personal Project 2015

11. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Creating the Plan
To meet my criteria, I planned to create
the following with the support of local
craftsmen and my own efforts:
1. The design and layout of the blocks themselves.
1. The packaging of the blocks.
1. The booklet that will come with the blocks.
1. A website for the blocks
1. My presentation script and slide show
I met many challenges along the way.
How I reacted to these challenges and what I
learned from them has developed me
a lot as an IB learner
Luke Hamilton, Personal Project 2015

12. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Creating the Blocks
I designed the blocks as 130 pieces to fit over 8
levels into a 26cm x 26cm box, and I made a
sample myself with styrofoam.
But getting the blocks made was a challenge!
I had to talk to five different craftsmen to finally get
to the two that could help me. Of those two, I was
able to get one at the quality that I wanted.
I tried different size and box types and in the
process settled on the best ones. The process
took longer than expected, but once I had a
chance to play with the final product, the
experience of creating with the blocks was also
beyond my expectation.
Luke Hamilton, Personal Project 2015

13. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Creating the Guide
Planning and creating the 16 page guide and
website allowed me to summarize my research
and think about how to explain the concept of
the Golden Ratio in the simplest and most
interesting way I could.
I used a printing company in Sanur to print the
guide, and I learned how to organize and brief the
printer on page numbers, paper size and paper
quality to ensure it looked professional.
Putting up a website also allowed me to see that
no one else had created a similar products. You
can visit it as www.fibonacciblocks.com and I was
very excited to see enquiries for the blocks come
through from the website (one for 5,000 sets!)
Luke Hamilton, Personal Project 2015

14. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Reflecting on my learning
How I have developed my planning, organising
and thinking skills
I have learned so much about myself from this
project. I decided early what my global context and
subject was going to be, but I still struggled as I
had not made a final decision on my product.
When I did, I found it a challenge to balance my
actions with my reporting, which led to difficulties.
These challenges grew as I began working with
the craftsmen and time frames changed.
From these, I learned to improve my balance, to
prioritise and plan better, to be flexible with
changes and to be constantly self-evaluating.
Luke Hamilton, Personal Project 2015

15. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Reflecting on my learning
How I have developed my information
literacy and research skills
I have also learned how much easier I learn when I
have picked a subject that I am very interested in.
By organising what I am learning and being clear
why I am learning it, I have become much better at
focusing my research skills.
I have also learned that I can get focused much
faster when I have examples to look at. For
example, having the Froebel Blocks as inspiration
and researching other IB oral presentations has
made it easier for me to grow my own confidence
in collecting the right information and knowledge to
support my own products and presentations.
Luke Hamilton, Personal Project 2015

16. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Reflecting on my learning
How I have developed my communication
and collaboration skills
Throughout the project I was concerned whether I
would be able to produce the finished product as I
knew it would require me working with craftsmen
and printers, giving them briefs and overseeing
their work.
To achieve this I have had to learn to improve my
communication and collaboration skills - especially
when it was not working. I have also learned how
much the success of this project has been the
result of me improving my collaboration skills with
my supervisor and the many people who have
helped me with this project.
Luke Hamilton, Personal Project 2015

17. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
Reflecting on the product
Comparing the product to
the criteria that I set
I am very pleased that the final product has met
the criteria that I set. The experience of the playing
with the blocks has been beyond my expectation.
This project has become my passion and I think I
could now branch out to different types of blocks.
They could have double sized and plush toys for
kids so that even when they’re young they can be
playing in golden proportions.
This personal project has really opened my
eyes as to what is possible when you take an
idea and turn it into a successful product.
Luke Hamilton, Personal Project 2015

18. Project Summary
Assistance Needed
I have created a set of wooden building blocks which are in the measurements of
the Fibonacci Sequence doubled (2,2,4,6,10,16,26). These blocks come with a
guide which helps to educate and inform about the Golden Ratio and the blocks.
These blocks help people of all ages appreciate complex concepts and better
identify connections and relationships between nature and technology/our society
as we know it.
A Final Word
I hope you enjoyed my presentation
and my product.
If you haven’t already played with the blocks then I
will have a stand open at the exhibition where you
can come and play with the blocks.
I will be selling these blocks as a product with
enough support in the near future so visit my site:
www.fibonacciblocks.com
to keep updated.
Luke Hamilton, Personal Project 2015

19. Thank you!
Luke Hamilton, Personal Project 2015