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Thales and the Pyramid

Thales (pronounced THAY-lees) 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
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

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This page revised   March 31, 2004
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