Golden Rectangles:
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Transcript of Golden Rectangles:
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Geometry Section 7-1D Geometry Section 7-1D
Golden RectanglesGolden Rectangles
Page 478Page 478You will need a calculator with You will need a calculator with
sin/cos/tan in sin/cos/tan in 1½ weeks.1½ weeks.
Freshmen - TI 30 XII S recommended. Around Freshmen - TI 30 XII S recommended. Around $15. You’ll need it for Alg. II.$15. You’ll need it for Alg. II.
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Golden Rectangles:Golden Rectangles:
Rectangle ACDF is a golden rectangle if and only if square ABEF with side lengths W makes rectangle CDEB
similar to rectangle ACDF.
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Golden Rectangles:Golden Rectangles:
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If you cut a golden rectangle into a square and a small rectangle, the small rectangle is also a golden
rectangle.
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Golden Rectangles:Golden Rectangles:
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All Golden Rectangles are similar.
If we calculate the ratio of the sides of all Golden Rectangles, we would
discover the Golden Ratio.
The Golden Ratio 1.618This is the ratio of the long side: short side.
Ratio of short side: long side
0.618
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“Donald Duck in Mathamagic Land” - 1959
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Try It:Try It:
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HIJK is a golden rectangle. Use an approximation for the golden ratio to find each length to the nearest tenth.
a. If IJ = 25, find JK.
25(1.618) 40.5
b. If HI = 10, find HK.
10(.618) 6.2
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Exercises:Exercises:
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Identify the golden rectangle.
b
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Exercises:Exercises:
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GHIF is a golden rectangle. Find each ratio.
1.618GHHI
.618GJJI
If GJ = 100, find JI to the nearest hundredth.
100(1.618) = 161.8
If GH = 25, find HI to the nearest hundredth.
25(.618) = 15.45
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Exercises:Exercises:
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Find the area of a golden rectangle whose width is 20. Then find the length and width of a golden rectangle that
has twice that area.
Area = length x width
32.36(20) = 647.2
If width = 20, then length = 20(1.618) = 32.36
A.R. = 2
S.R. = 2 1.41
Width = 20(1.41) = 28.2
Length = 32.36(1.41) = 45.63
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Exercises:Exercises:
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If you divide the length of a golden rectangle by its width, the number that you get is the golden ratio.
If you divide the length of a ______________by its width, the number that you get is the _____________.
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Homework: Practice 7-1DQuiz Tomorrow