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

[NateTheGreat]

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.

 

[tiny-tim]

Welcome to PF!

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?

 

[NateTheGreat]

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"?

 

[Sakha]

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"