Golden Rectangles:

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1 Geometry Section 7-1D Geometry Section 7-1D Golden Rectangles Golden Rectangles Page 478 Page 478 You will need a calculator with You will need a calculator with sin/cos/tan in sin/cos/tan in weeks. weeks. Freshmen - TI 30 XII S recommended. Freshmen - TI 30 XII S recommended. Around $15. You’ll need it for Alg. Around $15. You’ll need it for Alg. II. II.

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Geometry Section 7-1D Golden Rectangles Page 478 You will need a calculator with sin/ cos /tan in 1½ weeks. Freshmen - TI 30 XII S recommended. Around $15. You’ll need it for Alg. II. Golden Rectangles:. Pg. 478. - PowerPoint PPT Presentation

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Page 1: 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:

#1

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Identify the golden rectangle.

b

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Exercises:Exercises:

2-5

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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