A Ratio That Glitters Exploring Golden Ratios. Golden Ratio in Architecture The Pyramid of Khufu has...
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![Page 1: A Ratio That Glitters Exploring Golden Ratios. Golden Ratio in Architecture The Pyramid of Khufu has the Golden Ratio in the ratio of the height of the.](https://reader038.fdocuments.us/reader038/viewer/2022110208/56649da25503460f94a8f080/html5/thumbnails/1.jpg)
A Ratio That Glitters
Exploring Golden Ratios
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Golden Ratio in ArchitectureThe Pyramid of Khufu has the Golden Ratio in the ratio of the height of the pyramid with the length of half the base of the pyramid.
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Golden Ratio in Architecture
Measure from the base to the top and from the observation deck to the top
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Golden Ratio in Architecture
Read more: http://www.goldennumber.net/architecture/
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Fibonacci Review
• What’s the Fibonacci Sequence?0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89….
• How do you get it? What’s the pattern?Start the sequence with 0 and 1. Add the current term
to the previous term to get the next term.
• Where do we see this sequence?
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Fibonacci and Golden Ratio
• Take your graph paper and draw a 1 1 box around the middle of the page
• Draw another adjacent to it• Draw a 2 2 square adjacent to and below the
rectangle • Draw a 3 3 square adjacent to and to the left
of that rectangle
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Fibonacci and Golden Ratio
• Your drawing should look like this:
• Continue drawing squares in a clockwise direction until your paper runs out of space
• What do you notice about the pattern with the size of the squares?
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Constructing Golden Rectangles
Measure the length and width of each rectangle that was formed using the Fibonacci Sequence. The first three rectangles you should measure are highlighted in yellow below.
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Constructing Golden Rectangles
What do you notice about the ratio between the length and width of each rectangle as you measure
larger and larger rectangles?
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Golden Rectangle
F (phi) Is called the Golden Ratio.
Based on your work, what is a good approximation of ?
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Golden Rectangles Elsewhere
• The aspect ratio of YouTube videos• Ratio of length over width of photographs• Computer screens• Smartphone screens• Tablets
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Constructing Golden Rectangles
• Draw a square• Find the midpoint of the side of the square (A)
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Constructing Golden Rectangles
• Extend one side• Draw an arc of radius AB, centered at the
midpoint, and have it intersect the extended side of the square (C).
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Constructing Golden Rectangles
• Construct a perpendicular line at the intersection of the arc and the side.
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Constructing Golden Rectangles
• Extend the opposite side of the square to meet the new perpendicular line.
• Erase any unwanted markings.
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Constructing Golden Rectangles
Measure the dimensions. Is it a Golden Rectangle?
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Fibonacci and Golden Spiral
How is the Golden Spiral constructed?
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Golden Spiral in Nature
The Golden Spiral in nature: a nautilus shell