Easy scientific measurement

In summary: This is the geometric connection.In summary, there is a geometric connection between the 1/8 ratio of the shadow cast by a vertical pillar in Alexandria at noon during the summer solstice and the 1/8 ratio of the distance between Alexandria and Syene to the Earth's radius. This is explained by the well-known experiment conducted by Eratosthenes in 200 BC, which uses basic geometry to determine the Earth's circumference.
  • #1
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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  • #2
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:
 
  • #3


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"?
 
  • #4
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" [Broken]
 
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1. What is "Easy scientific measurement"?

"Easy scientific measurement" refers to the process of using instruments and techniques to collect data and quantify physical properties or phenomena in a simple and accurate manner. It involves selecting appropriate units, taking precise and accurate measurements, and analyzing the data to draw meaningful conclusions.

2. Why is accurate measurement important in science?

Accurate measurement is crucial in science because it provides quantitative data that can be used to test hypotheses, make predictions, and draw conclusions. It allows scientists to replicate experiments and compare results, leading to a better understanding of natural phenomena and the development of new technologies.

3. What are some common measurement tools used in science?

Some common measurement tools used in science include rulers, thermometers, graduated cylinders, balances, and microscopes. These instruments are designed to measure length, temperature, volume, mass, and other physical quantities with precision and accuracy.

4. How can I ensure accurate measurements in my experiments?

To ensure accurate measurements in your experiments, it is important to calibrate your instruments, use appropriate units, and minimize sources of error. It is also helpful to take multiple measurements and calculate the average to reduce the impact of random errors.

5. How can I convert between different units of measurement?

To convert between different units of measurement, you can use conversion factors or conversion tables. It is important to pay attention to the units and ensure that they cancel out correctly during the conversion process. Online unit converters and scientific calculators can also be useful tools for quick and accurate conversions.

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