Phi’s the Limit

Phi’s the Limit : 

Phi’s the Limit A WebQuest Art & Music Intro Resources Evaluation Wrap-Up & Conclusion Nature Human Body Fibonacci & Phi Student Examples

Introduction : 

Introduction The Golden Number – Phi φ What do sunflowers, ocean waves, photography and the human body have in common? Is it possible that our universe was created in such a way that a pattern is visible, almost as though there was some kind of order, rather than chaos? Could mathematics explain beauty in the world around us? All of you have heard of Pi (π), approximately 3.14...., an irrational number that is a constant that is the ratio of a circles circumference to its diameter and is used in formulas like the Area of a Circle and the circumference formulas of a circle.

Introduction : 

Introduction The Golden Number – Phi φ But have you heard of Phi (φ), approximately 1.618..., an irrational number that can be derived from the Fibonacci sequence? Phi, which is also known as the Golden Ratio is found in many places, including the human body, in nature and in music and in art! This WebQuest will help you discover nature’s golden number.

Introduction : 

Introduction The Golden Number – Phi φ But have you heard of Phi (φ), approximately 1.618..., an irrational number that can be derived from the Fibonacci sequence? Phi, which is also known as the Golden Ratio is found in many places, including the human body, in nature and in music and in art! This WebQuest will help you discover nature’s golden number.

Introduction : 

Introduction Task: Your task is to create a PowerPoint presentation that describes the Fibonacci sequence and shows how the Golden Ratio can be seen in the human body, nature and art.

Introduction : 

Introduction Process:Use these links to go through the five steps of the process to successfully complete your WebQuest. Each page has it's own set of instructions. As a group, assign jobs such as researcher, measurement, data collector, writer, etc. You will have five class periods to complete this assignment: 2-3 days to go through WebqQuest, research and collect data and 1-2 days to create your PowerPoint presentation.

Fibonaci & Phi φ : 

Fibonaci & Phi φ The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13... Each number in the sequence is obtained by taking the sum of the previous two numbers. Observe the sequence and find the next 20 terms (you will need your calculator.) Record your results in the Excel Spreadsheet. Check out the graph that is created as you put in these numbers. What do you observe? Create a slide in your PowerPoint that shows series starting with the numbers above and then listing the next twenty terms.

Fibonaci & Phi φ : 

Fibonaci & Phi φ Use your calculator to investigate the following relationship (record your results in Excel): Phi can be obtained by taking ANY two numbers and  adding them to make a third, (say 2 + 4 = 6), then adding the second and third to make a fourth, (4 + 6 = 10) then adding the third and fourth to make a fifth, (6 + 10 = 16) and so on. Do this process ten times. You should discover the following relationship: Take any two consecutive numbers in the sequence, divide the larger by the smaller, and the result should approximate 1.618. Is that true for your numbers? What do you notice as the numbers get bigger? Find out more at these links: The Golden RatioThe Golden MeanWikipedia Entry

Nature : 

Nature Find four items in nature that illustrate the Fibonacci series. (Check the resource links for websites and videos may be helpful as well as other links.) For example, when counting the number of petals of a flower, it is probable that they will correspond to one of the Fibonacci Numbers. It is seen that Lilies have 3 petals. Buttercups commonly have 5 petals.

Nature : 

Nature Take pictures (or use public domain images found online) to create four slides in your PowerPoint. Set up your slides so that at the picture is shown on the left and the description of how it illustrates the Fibonacci Series and Golden Mean is on the right. (if you use images you found online, please include a link to the original website on your slides) Find out more information at these links:In Nature

Human Body : 

Human Body Take measurements in millimeters of the arm (elbow joint to wrist) and hand (wrist to tip of longest figure) of 10 classmates, parents and/or school personnel. Measure as accurate as possible and record your results in the Excel sheet (use the Human Body Experiment Sheet). Write a formula to divide the arm length by the hand length for each of the ten people you used in this experiment. Write a formula to find the average of these numbers.

Human Body : 

Human Body Insert a text box in your excel sheet describing what the average of these ratios. Does your average point to the Fibonacci series or Golden Mean being found in the human body? Tell in your text box why or why not. Search the resources (and check out the video link) for other examples of the Fibonacci series and Golden mean in the human body. Copy one picture onto your excel sheet and insert a text box to describe the connection. Find out more at this link: In the Human Body

Human Body : 

Human Body Play with the math by using this interactive. Find out more at this link: The Beauty of Math

Arts & Music : 

Arts & Music Artists throughout history and in many different cultures have found the ratio of 1 to 1.618 is aesthetically pleasing. This ratio can also be obtained by dividing a line so that the short and long pieces have the same proportion (1 to 1.618) as the long piece does to the length of the original line. Use the resources given to discover three artistic applications of the Golden Mean (Golden Triangle, Golden Rectangle). Re-create the golden rectangle-spiral by hand.

Arts & Music : 

Arts & Music Use pictures found online to create three slides in your PowerPoint. Set up your slide so that the picture is shown on the left and the description of how it illustrates the Fibonacci Series and Golden Mean is on the right. (if you use pictures you got online, please include a link to the original website on your slides) Your sketch of the golden rectangle can be one of the three slides.

Arts & Music : 

Arts & Music Check out these links:PhotographyPhotography 2

Wrap It Up : 

Wrap It Up Create an Introduction slide. On your introduction slide, write a short paragraph introducing your project (You may want to include historical information.) Create a Conclusion slide. Choose one of the following questions to conclude your PowerPoint presentation or make up your own:

Wrap It Up : 

Wrap It Up Now that you have an understanding of the world around you, can you think of any other areas you may find the Golden Ratio? Do you know any architects, musicians, artists, financial advisors or others who use this ratio? If you do, discuss this ratio with them What is your opinion to Phi’s application in your world or to the meaning of life? What was most fascinating to you about this topic?

Evaluation : 

Evaluation Click on the link to view the rubric for this project.

Resources : 

Resources http://britton.disted.camosun.bc.ca/fibslide/jbfibslide.htm http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html http://photoinf.com/Golden_Mean/ http://www.vashti.net/mceinc/golden.htm http://en.wikipedia.org/wiki/Fibonacci http://fmphotocourses.blogspot.com/2006/10/advanced-composition-and-golden-ratio.html http://www.miqel.com/fractals_math_patterns/visual-math-phi-golden.html http://goldennumber.net/ http://delicious.com/bismith/golden_ratio http://www.youtube.com/watch?v=-ncEEXekZek&feature=related (Golden Rectangle – Mathtv.com) http://www.youtube.com/watch?v=_NmSEEhtc1U&feature=related (Fibonnaci Sequence – Mathtv.com) http://www.youtube.com/watch?v=TgSXyi-x8mY&feature=related (Golden Ratio World) http://www.youtube.com/watch?v=rcF-Ju6hqTI&feature=related (Tool-Lateralus & Fibonacci Sequence – Music) http://www.youtube.com/watch?v=N6RMQy7pBtM&feature=related (God’s perfect universe Pt. 1) http://www.youtube.com/watch?v=SD-ZiqDvnKo&feature=related (from BBC documentary – understanding “beauty”) http://www.mathsisfun.com/numbers/golden-ratio.html

Student Examples : 

Student Examples Embedded Podcast (created in Movie Maker)