Is There a Geometric Link Between the Ratios in Eratosthenes' Experiment?

AI Thread Summary
The discussion centers on the geometric relationship between the shadow of a pillar in Alexandria and the distance between Alexandria and Syene, both of which are in a 1-to-8 ratio. It is noted that during the summer solstice, the sun is directly overhead in Syene, which is crucial for understanding the experiment conducted by Eratosthenes. Participants express curiosity about the meaning of a "geometric connection" between these ratios. A simulation of the experiment is shared to illustrate the underlying geometry. The conversation emphasizes the significance of these observations in understanding Earth's dimensions.
NateTheGreat
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Homework Statement



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?

Homework Equations



Not sure exactly what kind of answer they are looking for here.
 
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NateTheGreat said:
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! :smile:

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 :wink:)

Does that help? :smile:
 


tiny-tim said:
Hi NateTheGreat! Welcome to PF! :smile:

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 :wink:)

Does that help? :smile:

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

http://www.edumedia-sciences.com/a287_l2-eratosthenes-experiment.html"
 
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