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

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Homework Help Overview

The problem involves a geometric exploration of the ratios observed in Eratosthenes' experiment, specifically relating to the shadow cast by a pillar and the distance between two locations on Earth. The context is rooted in geometry and historical methods of measuring the Earth's circumference.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the significance of the 1-to-8 ratios in the context of the shadow and distance measurements. Questions arise about the meaning of a "geometric connection" between these ratios and the implications of the sun's position during the experiment.

Discussion Status

The discussion is ongoing, with participants providing contextual information about the experiment and exploring the geometric relationships involved. Some guidance has been offered regarding the sun's position, but no consensus has been reached on the nature of the geometric link.

Contextual Notes

Participants note the importance of the sun being directly overhead at Syene during the summer solstice, which may influence the interpretation of the ratios. There is also mention of a simulation that illustrates the experiment's geometry, suggesting a resource for further exploration.

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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