Fibonacci Numbers and the Golden Section
This excellent site contains a large and interesting selection of material on Fibonacci Numbers and their myriad related concepts. It includes web and text references to the rich literature of Fibonacci numbers. It also features a variety of images, graphics and animations. Many of the topics include student investigations for NCTM standard type explorations. The content includes standard motivational examples and applications in nature, but...Show More
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like this site. This site deals with other kinds of Math. For instance,many
puzzles in dealing with nature and animals to try like the honeybees where
numbers add together to make a certain group. The number Trick is a must to try
under Mathematical Magic Fibonacci Numbers. It gives a very good explanation and
a formula on how to do it. So you pick any two numbers add plus the new number
ten times and try it with your friends. Also, working with triangles in making a
number pattern inside the triangle. And,you can try doing a family tree.
Also,numbers dealing with prime numbers and factors I found that this part was
difficult to understand the pattern of numbers. However, there was a table of
numbers was easier to see the process.As well as towards the end of each puzzle
it gives an option if you like for Things To Do so you can try it yourself. And,
they are also great pictures included for each puzzle. So, if you like doing
puzzles and nature then you would enjoy this site. Also,any of you teachers out
there it is great tool because they can work with their students in groups
dealing with patterns and numbers. I enjoyed viewing this site for about an hour
in solving these puzzles.
site. While I was trying the problems it was easy to get to the next page and
move back to the begining. There was no conflict like the site dissapeared or I
couldn't get the page up on screen.
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quality of the material is great and written so you can understand it. This is
an excellent resource to aid teacher's in teaching this subject and it does
enhance learning capablities.
and learn. With Merlot and a regular search engine the Fibonacci site was easy
to access for me and I'm sure it would be for first time users as well.
Steven Vidal (Student)
minutes looking over and reading it. I thought that all of the information was
very useful and very descriptive as well. I tried taking down some important
notes and began writing down some of the bold letter words.
As I was reading all of the material that was given to me I realized that
most of the information helped me to understand what a real Fibonacci number was
and what it represents. All of the concepts that were brought up in this site
were very descriptive and very educational as well. I thought that all of the
information was educationally significant because it gave certain models and
explinations of what a student was trying to look at or find.
I think that the students learning will be enhanced if they choose to look
at this site because of the simple fact that it gives a great meaning to what
students are trying to find. This site also gives great understanding to all
the material as well. Once a student takes a look at what they are trying to
study, they will find that these sites will be very helpful to them no matter
I also believe that first time users will find this technique very easy to
use and go by because it gives so many different examples and notes to
understand the material.
Nicky Thortis (Student)
reading The Davinci Code, by Dan Brown and the Fibonacci Numbers were used as a
cypher in two different situations. This topic is quite fascinating and I
really like how this website depicted feasible ideas of this concept. The
Golden Number was also discussed, which I found equally as intriguing. Again it
was great to see that almost everything in nature correlates with the golden
I spent about 30 minutes browsing this topic and think it has given me a great
topic for my final research paper!
and clearly depicted so it is very easy to follow along. I think everyone
should easily be able to grasp this concept as described on this web page. It
was very effective.
Vincent Klumper (Student)
Fibonacci number was, and had no idea how the golden setion worked. This sit I
feel was very educational, and I also have to say it was very easy to follow.
So I enjoyed this sit a lot.
hard not to be confusing, but maybe there can be a more fun approuch to the
michael bertoldo (Student)
the site, but the inexperience of the user. i did spend some time on the
fibonacci numbers, specificaly the the rabbits and reproduction. this section
and its visual content made it interesting and easy to understand. i feel the
general effectiveness is good and that the overall learning potential for both
students and teachers is high.
liked the areas i viewed because the were visual and easy to understand. if
fiist time users are proficient on the computer and the internet
Ryan Hendry (Student)
understand. I went through it for about 15 mins and looked at some of the
puzzles and listened to an audio play on the golden section.
The material seemed to be pretty accurate on the goldon section, at least
from what I have learned in my math class. It helped me to grasp a better
understanding of the concepts.
This site seemed like a pretty legitimate site for use as a teaching tool.
I think it could be a good tool.
The materials were very user friendly.
Matt Imwalle (Student)
Before I read this page I never even heard of a Fibonacci number or sequence.
But now after this I have an extremely good awareness of what they are now. I
liked the examples that they used on this page, how many bunny rabits can be
produced in a given time and the whole bumble bee thing. I never knew that
rabbits can reproduce after a month. Then the examples with the bee's the male's
compared to the female's were very cool. I tried the Fibonacci sequence for
myself by doing the diagram and following all the directions it says. This
material accurately presents concepts and models that are very good for
educational purposes. They break it down and explain it with out confusing you.
The models are good and also are not confusing. After reading this I now know
what the Fibonacci numbers are and how the Fibonacci Sequence appears in nature.
concept. I tried to follow along, rereading certain sections, but had very
little luck understanding.
many pictures and examples as it did. Even though I couldn't understand it I
still gave it a four: I think that the material was well organized and I'm sure
would make perfect sense to a more mathematically inclined individual. The
pages go into great detail about the subject and present the material in a
number of different ways. I found the section on the Golden Section in Nature
to be interesting and some of that made sense but apparently, Fibonacci numbers
are not for me. I am sure that the material was presented accurately and that
this is educationally significant. The author gave examples and backed them up
with proofs and pictures/diagrams. I don't know if this would be the best
"candidate" for enhancing learning and teaching, but that is strictly based off
of my own experience with the material and this is not to say that others
wouldn't benefit from it. I suppose it would be fine to use if the words were
put a little more simply. The software was easy to use and the links were easy
Marcela Alcorn (Student)
say I spent about 20 minutes really grasping all the information I could take
in. This web site was extremely easy to use and to get around. I loved
everybit of this site. The thing that struck me most was not necessarily the
math, but being a visual person, the pictures showed how it could be used in a
different scenario other then numbers and art. The golden section was already
fascinating for me, but to see how they provided different images and
explanations, this made my experience even better than originally expected.
Overall to get to the site was a bit difficult but after a couple of minutes
fooling around, you'd get the hang of it.
amy konsterlie (Student)
liked the animation regarding the circular spiral moving within the daisey-like
shape. So much of nature relates to the Fabonacci Numbers and the Golden Section
gave good examples of concepts to this type of math, making it easy to
understand how the math can be used. There was not alot of applications on the
site. It had educational purpose on puting projects togeather.
Kathy Phelan (Student)
software. I'm embarrassed to admit I did not know what Fibonacci numbers are.
I just like the name, Fibonacci. Once I arrived, the simple explanation of what
Finonacci numbers are fascinated me (I guess it's easy to fascinate me). I
immediately thought, "how cool!" I went to the link that was mentioned in terms
of introducing one to the site and was drawn to the animals. I could spend
hours on this site. In fact, I may go back. Who or what is Fibonacci? I
actually figured out the rabbit problem. The visuals were great and having the
answer available is even better. Thank you.
Terence Telkamp (Student)
fairly well. I liked that right away it showed what the Fibonacci secuence,
golden section numbers, and the golden ratio all were. Then I told where to go
to get a basic understanding of the ideas.
site does a good job at showing even someone like me how these concepts might be
useful or applied.
ex. rabbit family trees, or packing to save on wasted space
a few minutes looking through a few of the examples and found them fun as well
as useful in math. this was on way to find patterns in sets of numbers. the
brink example and the honeybee demonstration was very cool because they had
visual that made it much easier for me to understand. i think this is a good
site for some to look at in order to make some aspects of this math simpler.
R. Lynn Sanitate (Student)
necessarily the history behind Fibonacci but the section on Numbers and Nature.
Since I have an appreciation for nature I am more inclined to gather my
information here. Mathematics? surrounds me and I haven?t been able to recognize
it. Fibonacci has my attention.
This site offers plenty of resources ? enough to make your head spin. My second
time exploring this site kept me busy for a couple of hours. If you have
difficulty understanding math and love nature this is the place to come.
helps. There are convent tools such as calculators, charts and graphs that
assist in understanding mathematical principals.
Beatriz Solorio (Student)
Clara California. When visiting the Fibbonacci web site it took me
approximately an hour to read. This was due to the fact that I took time in
reading what I thought was interesting. I gave this site the highest score
because I thought that it really was informative and actually fun to learn.
This site focused on a series of numbers called Fibbonacci. It was interesting
to find out were this idea came from, and how these numbers are found in nature.
It also introduced the idea of "phi" the Greek representation of 1.61804....
The pictures were one of the best parts of this site; they really helped in
understanding the concept.
Tatiana Sviridovsky (Faculty)
Brian Doore (Student)
just the first time. I'm sure I'll be back many times. It is like math
play-land. The first time I heard of Fibonacci numbers and the golden section
was when I saw a Disney producion called "Donald Duck in Mathamagic land" or
something like that. It was a long time ago. The program and its treatment of
these topics has made a lasting impression on me. I was very pleased to see
those two topics together on one website. I know I only saw the tip of the
iceberg here. The site and its links seem endless. I especially enjoyed the
Fibonacci puzzle section, although I have only visited the simple games thus
far. I can see why this is an award winning site.
it technically, except that as a learning tool, it is very effective.
Thuy Pham (Student)
and more than 2hrs to review the materials on the site. The site is so large. It will take alot of time to cover every single information. I think this web-site is very useful for enhancing teaching and learning. The quality of material content is perfect. We can find most of valued informations we need about Fibonacci Numbers and The Golden section. I love the way they arranged the pages. The informations, formulars, examples, explainations, sources,etc are conected. Web- links and references are powerful. Especially, the website was designed very organization with interested graphics; thus,that makes the users are quite persuaded and actracted. The direction is clear and helpful for users easy to enter the entire pages. The materials are written simple, easy to read and understandable. It is excelent site, and suitable for different levels of background knowledge.
Christopher Black (Student)
I've spent 15 minutes following the links and the trail of information. Feasting
on examples and charts. The links to outside sites are just as good. I think
this site will do well to instruct the expert as well as the intermediate. There
is such a wealth of information that you'd be hard pressed to not go away withs
some deeper understanding.
Alicia Merino Gamboa (Teacher (K-12))