Thales and the Pyramid Thales (pronounced THAYlees) is regarded as the father of Greek philosophy and mathematics. Sometime around the year 600 BC, he visited Egypt to study geometry. There is a legend which says that Thales impressed the Egyptians by calculating the height of the pyramid at Giza.
A 30 inch stick held vertically from the ground at 3 PM cast a 36 inch shadow, while at the same time the pyramid cast a shadow 100 feet beyond its base. At 4 PM, the same stick had a 45 inch shadow, while the pyramid's shadow extended 210 feet beyond its base.
How high was the pyramid?
Let x represent t ½ the width of the pyramid. The shadow was measured only past the edge of the pyramid.
Then use proportion to solve for x, using the two time differences: (x+100) / 36 = (x+210) / 45 x=340 Let y= the height of the pyramid. Then, using the newly found x, find the height of the similar triangles at the same time of day, using proportion: (340+100) / 36= y / 30 y=366.66
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