Thales

Thales' Shadow How Thales Measured the Height of the Great Pyramids

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Similar Triangle Theorem ,[object Object],[object Object],a a b b c c Similar Triangles: 1) 2)

Ratios of Similar Triangles ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],a d b c f Similar Triangles: (1) (2) e

Calculations ,[object Object],[object Object],[object Object],[object Object],[object Object],a d b c f Similar Triangles: (1) (2) e

Calculations (continued) ,[object Object],[object Object],[object Object],a d b c f Similar Triangles: 1) 2) e

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Thales’ Shadow ,[object Object],[object Object],l a a = l

The Pyramid’s Shadow ,[object Object],h = b

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Example l a From the similar triangle theorem : a / l = h / b Thales was 6 feet tall, his shadow was 4 feet long, and the pyramid’s shadow had a base with side equal to 100 feet long at the same time of day. How high is the pyramid? Expressed Mathematically: 6 / 4 = ? / 100 The pyramid’s shadow is 25 times longer than Thales’ shadow because 100 ft. / 4 ft. is 25. According to the similar triangle theorem, if side b is 25 times longer than side l then side a must be 25 times longer than side h. So, 6 ft. x 25 = the height of the pyramid = 150 ft. Does 6/4 = 150/100? Yes

Accuracy of Shadows ,[object Object],[object Object],[object Object],[object Object]

Time For Fun! ,[object Object],[object Object]

Thales

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Thales