# Easy scientific measurement

by NateTheGreat
Tags: measurement, scientific
 P: 4 1. The problem statement, all variables and given/known data The Shadow cast by a vertical pillar in Alexandria at noon during the summer solstice is found to be 1/8 the height of the pillar. The distance between Alexandria and Syene is 1/8 the Earth's radius. Is there a geometric connection between these two 1-to-8 ratios? 2. Relevant equations Not sure exactly what kind of answer they are looking for here.
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P: 25,464
 Quote by NateTheGreat The Shadow cast by a vertical pillar in Alexandria at noon during the summer solstice is found to be 1/8 the height of the pillar. The distance between Alexandria and Syene is 1/8 the Earth's radius. Is there a geometric connection between these two 1-to-8 ratios?
Hi NateTheGreat! Welcome to PF!

You've left out that at noon during the summer solstice, the sun at Syene is directly overhead.

(I know that 'cos this is a well-known experiment by Eratosthenes in about 200 BC )

Does that help?
P: 4
 Quote by tiny-tim Hi NateTheGreat! Welcome to PF! You've left out that at noon during the summer solstice, the sun at Syene is directly overhead. (I know that 'cos this is a well-known experiment by Eratosthenes in about 200 BC ) Does that help?
Ah! So then would that explain why they are both 1/8 of the Earth's radius? I'm trying to figure out what they mean by a "geometric connection"?

P: 295

## Easy scientific measurement

Look at this flashy simulation of the experiment, it is a demo but you can see from it the basic geometry used.

Here

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