1. The Beauty of the Golden Ratio
Presented by:
Nikki Pizzano
Danielle Villano
Tanya Hutkowski
Pedagogy Conference April 2009

2. Beauty or Beast? A B
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3. Activote Activity A B
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4. Let’s Get Started Width of the face Top of the head to the chin
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5. Width of the nose
Length of lips
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6. Nose tip to chin
Lip to chin
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7. Analyze the Results
Let’s take a closer look at these measurements in Excel.
Pedagogy Conference April 2009

8. Linking Beauty To Phi
Also known as the golden number
Phi is an irrational number which is found in all aspects of nature, and supposedly using it as a proportion leads to the most beautiful shapes.
Many of the ancient Greek sculptors and builders used to use it.
Pedagogy Conference April 2009

9. Finding the Gold Pedagogy Conference April 2009
a = Top-of-head to chin
b = Top-of-head to pupil
c = Pupil to nose tip
d = Pupil to lip
e = Width of nose
f = Outside distance between eyes
g = Width of head
h = Hairline to pupil
i = Nose tip to chin
j = Lips to chin
k = Length of lips
I = Nose tip to lips
Pedagogy Conference April 2009

10. The Beauty Test http://www.intmath.com/Numbers/mathOfBeauty.php
This mask of the human face is based on the Golden Ratio. The proportions of the length of the nose, the position of the eyes and the length of the chin, all conform to some aspect of the Golden Ratio.
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11. How Phi is their Face?
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12. How Phi Are They?
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13. The Greeks knew this as the Golden Section and used it for beauty and balance in the design of architecture.
The Renaissance artists knew this as the Divine Proportion and used it for beauty and balance in the design of art.
The Fibonacci series appears in the foundation of many other aspects of art, beauty and life. Even music has a foundation in the series, as 13 notes make the octave of 8 notes in a scale, of which the 1st, 3rd, and 5th notes create the basic foundation of all chords, and the whole tone is 2 steps from the root tone.
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14. d i a m e t r to
circumference
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15. y x
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16. 1 x 1 1
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17. We can solve this quadratic equation using the Quadratic Formula.
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18.
where a = 1
b = 1
c = -1
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19. Pedagogy Conference April 200919

20. …which can be substituted into the ratio :
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21. How did the ancient Greeks use the Golden Mean?
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22. Size your compass to be the length of one side of the square
Given square ABCD.
Size your compass to be the length of one side of the square
Make a small arc above segment AB and one below segment AB
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23. Place the point of your compass on point B and repeat.
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24. Place your ruler on the intersections of the arcs.
Make a mark on segment AB and segment CD.
These are the midpoints of the segments.
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25. Mark points E and F at the midpoints of segments AB and CD.
Use your ruler to create a segment from point C to point E.
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26. Repeat, creating segment BF
Pythagorean Theorem:
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27. Pythagorean Theorem: c b a b c a
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28. Use your ruler to extend segments AB and CD.
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29. Adjust your compass so that it is the length of segment CE
Make a mark on the extension of segment AB.
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30. Place the point of your compass on point F.
Make a mark on the extension of segment DC.
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31. Create points GH and finish the rectangle by using your ruler to create segment GH.
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32. The rectangle you have created is the golden rectangle.
Segment DE = 1/2
Segment EF =
Segment DF =
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33. This rectangle is proportional to our original rectangle.
If we make a square in the remaining rectangle, you will again see one rectangle left.
This rectangle is proportional to our original rectangle.
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34. We could continue doing this over and over in a never ending pattern.
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35. phi = …
(Smaller/Larger)
Phi = …
(Larger/Smaller) 1 1 2 3 5 8 13 …
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37. Pop Quiz!! a. in the human face b. in the Parthenon c. in DNA
Where can the golden ratio be found?
a. in the human face
b. in the Parthenon
c. in DNA
d. all of the above
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38. Question 2
Which is the closest approximation of the Golden Ratio?
a …
b …
c …
d. 3:00
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