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
Messages
4
Reaction score
0

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.
 
Physics news on Phys.org
Welcome to PF!

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"
 
Last edited by a moderator:
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Eratosthenes' Measurement of Earth's Circumference
Replies
10
Views
16K
Problem involving ratios to find the length of a shadow
Replies
1
Views
13K
Circumference of Earth With Eratosthenes
Replies
4
Views
3K
How Does Relativity Affect the Measured Distance Between Cities at High Speeds?
Replies
17
Views
2K
Determining the Radius of the Moon (Ratio and shadow measurements)
Replies
2
Views
3K
Ratio between molecules having different speeds
Replies
2
Views
1K
Gravitation: Mass Ratio, Separation, and Potential Maximum
Replies
3
Views
2K
Maximizing Energy Efficiency: Calculating Tabeshband Width and Window Height
Replies
1
Views
2K
At Home Experiments to Prove Scientific Facts
Replies
25
Views
3K
Angle between line and its shadow on a plane
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top