Does the Great Pyramid contain the Golden Ratio

Does the Great Pyramid contain the Golden Ratio -...

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Does the Great Pyramid contain the Golden Ratio? Dividing slant height s by half base gives 186.369 ÷ 115.182 = 1.61804 which differs from (1.61803) by only one unit in the fifth decimal place. The Egyptian triangle thus has a base of 1 and a hypotenuse equal to . Its height h , by the Pythagorean theorem, is given by h 2 = 2 - 1 2 Solving for h we get a value of . Project: Compute the value for the height of the Egyptian triangle to verify that it is . Thus the sides of the Egyptian triangle are in the ratio Kepler Triangle The astronomer Johannes Kepler (1571-1630) was very interested in the golden ratio. He wrote,
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Unformatted text preview: "Geometry has two great treasures: one is the theorem of Pythagoras, the other the division of a line into mean and extreme ratios, that is , the Golden Mean. The first way may be compared to a measure of gold, the second to a precious jewel." In a letter to a former professor he states the theorem, which I rephrase as: If the sides of a right triangle are in geometric ratio, then the sides are We recognize this as the sides of the Egyptian triangle, which is why its also called the Kepler triangle. Project: Prove that If the sides of a right triangle are in geometric ratio, then the sides are...
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This note was uploaded on 11/05/2011 for the course ARH ARH2000 taught by Professor Karenroberts during the Fall '10 term at Broward College.

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