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Golden Rectangles:

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.

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Golden Rectangles:

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  1. Geometry Section 7-1D Golden RectanglesPage 478You 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.

  2. Golden Rectangles: Pg.478 Rectangle ACDF is a golden rectangle if and only if square ABEF with side lengths W makes rectangle CDEB similar to rectangle ACDF.

  3. Golden Rectangles: If you cut a golden rectangle into a square and a small rectangle, the small rectangle is also a golden rectangle. Pg.478

  4. Golden Rectangles: All Golden Rectangles are similar. If we calculate the ratio of the sides of all Golden Rectangles, we would discover the Golden Ratio. Pg.479 The Golden Ratio » 1.618 This is the ratio of the long side: short side. Ratio of short side: long side » 0.618

  5. “Donald Duck in Mathamagic Land” - 1959

  6. Try It: HIJK is a golden rectangle. Use an approximation for the golden ratio to find each length to the nearest tenth. Pg.479 a. If IJ = 25, find JK. 25(1.618) » 40.5 b. If HI = 10, find HK. 10(.618) » 6.2

  7. Exercises: Identify the golden rectangle. #1 Pg.480 b

  8. Exercises: GHIF is a golden rectangle. Find each ratio. GH HI GJ JI 1.618 .618 2-5 Pg.480 If GH = 25, find HI to the nearest hundredth. 25(.618) = 15.45 If GJ = 100, find JI to the nearest hundredth. 100(1.618) = 161.8

  9. Exercises: 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. If width = 20, then length = 20(1.618) = 32.36 7 Pg.480 Area = length x width 32.36(20) = 647.2 A.R. = 2 S.R. = Ö2 » 1.41 Width = 20(1.41) = 28.2 Length = 32.36(1.41) = 45.63

  10. Exercises: If you divide the length of a ______________by its width, the number that you get is the _____________. If you divide the length of a golden rectangle by its width, the number that you get is the golden ratio. 8 Pg.480

  11. Homework: Practice 7-1DQuiz Tomorrow

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