The following thought provoking ideas have been shared with me by others. Try answering one or more of the bonus questions. Send your answers (remember to include the queston you are answering and your school information!) to heratos@youth.net. And, if you have an idea for a bonus question, send it to me, jmeinke@en.com.

Logic of the Assumptions:

It's curious to note that Eratosthenes had other reasons for believing that the Earth was round and that the Sun's rays were "essentially" parallel. As a bizarre twist, he could have reversed these assumptions ("The Earth is flat, and the Sun is essentially a single point with its rays being radians") and estimated the distance between the Earth and Sun.

1. What's wrong (or right) about these reversed assumptions?

2. Would the estimate of the distance be "accurate?" Why or why not?

Accuracy & Precision:

The Sun's rays aren't "perfectly" parallel. And the Earth isn't "perfectly" round. And Eratosthenes & Co., didn't have perfect synchronization (timing) for their experiment.

1. Does "essentially parallel" mean "exactly parallel" or just "parallel enough?"

2. What would happen if the Sun were really a single point? What if it were really much closer to the Earth? Would these changes affect Eratosthenes' assumptions? Why or why not? Can you redesign the experiment to adjust for the changed assumptions?

3. What are the sources of error in the techniques used in the measurements?

4. What changes might make the readings more "exact?"

5. Does timing of the experiments really matter?

Other Eratosthenes Calculations

Once Eratostheses determined the circumference of the earth, he devised a method for determining

1. The diameter of the moon.
2. The distance between the earth and the moon.