Introduction
Ok students, we have just finished up our class research project about Fibonacci and his wonderful set of numbers: 1, 1, 2, 3, 5, 8, 13, 21, …. We learned that Leonardo of Pisa was really onto something when he started studying this magical set of numbers with his “rabbits” problem. Now it’s time to solve the mystery of …”The Golden Ratio.” We are going to take this set of numbers we discovered and we are going to find out the special relationship and patterns that are hidden. After that, we are going to search and see if we can find these patterns in our everyday life. Let the journey to the past begin …..
Ok students, we have just finished up our class research project about Fibonacci and his wonderful set of numbers: 1, 1, 2, 3, 5, 8, 13, 21, …. We learned that Leonardo of Pisa was really onto something when he started studying this magical set of numbers with his “rabbits” problem. Now it’s time to solve the mystery of …”The Golden Ratio.” We are going to take this set of numbers we discovered and we are going to find out the special relationship and patterns that are hidden. After that, we are going to search and see if we can find these patterns in our everyday life. Let the journey to the past begin …..
Task
There are many different theories about exactly when and where this “golden ratio” was discovered, and by whom it was discovered. Your job is to travel through time and figure out this mystery for yourself. You will work with a partner and create a two page (double spaced) report on The Golden Ratio with your interpretation of this mystery through the provided resources (including what is Phi-how did you come up with the numbers, who you think really discovered it, when it was discovered). In this report you will include any graphs and calculations that you discovered along the way. Also included with your report, each group will create a *poster board (22” x 28”) with a visual representation of what you have discovered, as well as a reference of at least 5 examples you can find The Golden Ratio out in the world. This project should be completed in a neat and organized way to show that you clearly understand the concepts and mysteries of Phi and The Golden Ratio.
* one poster board will be provided for each group … please take good care of this because it is the only one that will be given from the teacher.
There are many different theories about exactly when and where this “golden ratio” was discovered, and by whom it was discovered. Your job is to travel through time and figure out this mystery for yourself. You will work with a partner and create a two page (double spaced) report on The Golden Ratio with your interpretation of this mystery through the provided resources (including what is Phi-how did you come up with the numbers, who you think really discovered it, when it was discovered). In this report you will include any graphs and calculations that you discovered along the way. Also included with your report, each group will create a *poster board (22” x 28”) with a visual representation of what you have discovered, as well as a reference of at least 5 examples you can find The Golden Ratio out in the world. This project should be completed in a neat and organized way to show that you clearly understand the concepts and mysteries of Phi and The Golden Ratio.
* one poster board will be provided for each group … please take good care of this because it is the only one that will be given from the teacher.
The Process
Think about what we discovered when we worked out Leonardo of Pisa’s “rabbit” problem. We found the pattern of simply adding the prior two numbers together to get the next one in line. It’s time to expand on this and find the incredible patterns and mysteries involved.
Think about what we discovered when we worked out Leonardo of Pisa’s “rabbit” problem. We found the pattern of simply adding the prior two numbers together to get the next one in line. It’s time to expand on this and find the incredible patterns and mysteries involved.
- How
could you figure out the algebraic equation for this number sequence?
- Is
there a relationship between the prior two numbers and the next one in line,
besides adding them together?
- How did Leonardo come up with the “rabbit”
problem in the first place?
- Was
this series of numbers used before Leonardo was even born?
- How
far back does this mystery go?
- Besides
math, what other things have used this ratio?
- What
came first, the ratio or the objects we found them in?
- Can
you find anything outside your front door or even in the “mirror” that uses
this ratio?
- What
is the coolest thing you have learned about this sequence of numbers?
- What
is the coolest thing you have seen that uses The Golden Ratio?
Resources
The past is a vast vacuum of volume and velocity! To help you along your journey, I have provided you with several stopping points to rest your eyes and your mind!
The past is a vast vacuum of volume and velocity! To help you along your journey, I have provided you with several stopping points to rest your eyes and your mind!
- Math is Fun - Here you will find help with figuring out the secrets of The Golden Ratio.
- Golden Number - We can find other places besides math where Phi is used.
- Wikipedia - Always a helpful resource, Wiki can show you a path to the past.
- EyePhi - An interesting website that could lead to a plethora of possibilities.
- Natures-Word - A wonderful visualization of the magical number.
- Plus Math - Here you can read all about our friend Leonardo of Pisa.
- Geom - More examples of the Golden Ratio in the world around us.
Conclusion
Whew! Traveling back in time sure is hard work! What did we discover? The Golden Ratio is everywhere! It’s in flowers, animals, trees, and even people. Where else can we find this miracle number? How can we use this in our adult lives? The next time you hear a song, or see a painting, smell a flower, or even see a snail … you will remember the little Italian guy … Leonardo of Pisa and wonderful rabbits!
Whew! Traveling back in time sure is hard work! What did we discover? The Golden Ratio is everywhere! It’s in flowers, animals, trees, and even people. Where else can we find this miracle number? How can we use this in our adult lives? The next time you hear a song, or see a painting, smell a flower, or even see a snail … you will remember the little Italian guy … Leonardo of Pisa and wonderful rabbits!
Images provided by:
Math is Fun
Pinterest
Natural Organization
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This template is based on the original WebQuest template. To learn more about WebQuery, visit The WebQuery
Math is Fun
Natural Organization
We all benefit by being generous with our work. Permission is hereby granted for other educators to copy this WebQuery, update or otherwise modify it, and post it elsewhere provided that the original author's name is retained along with a link back to the original URL of this WebQuery. On the line after the original author's name, you may add "Modified by (your name) on (date)". If you do modify it, please let me know and provide the new URL.
This template is based on the original WebQuest template. To learn more about WebQuery, visit The WebQuery