Geometric Construction of the Golden Ratio

# Geometric Construction of the Golden Ratio - Triangle It is...

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Geometric Construction of the Golden Ratio Subdivide a square of side 1 into two equal rectangles. Then lay out a distance equal to the diagonal of one of these half-squares, plus half the side of the original square. The ratio of this new distance to the original side, 1, is the golden ratio. Project: Do this construction for the golden ratio. Project: Mathematically show that this construction gives the golden ratio. Egyptian Triangle Let's now return to the pyramids. If we take a cross-section through a pyramid we get a triangle. If the pyramid is the Great Pyramid, we get the so-called Egyptian
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Unformatted text preview: Triangle. It is also called the Triangle of Price, and the Kepler triangle . This triangle is special because it supposedly contains the golden ratio. In particular, the ratio of the slant height s to half the base b is said to be the golden ratio. To verify this we have to find the slant height. Computation of Slant Height s The dimensions, to the nearest tenth of a meter, of the Great Pyramid of Cheops, determined by various expeditions. height = 146.515 m, and base = 230.363 m Half the base is 230.363 ÷ 2 = 115.182 m So, s 2 = 146.515 + 115.182 2 = 34,733 m 2 s = 18636.9 mm...
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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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