Cette webquest a permis aux élèves des différents pays de confronter leurs mesures et de calculer le meridien terrestre

1. Follow the path of Eratosthenes
In Egypt, about 2200 years ago, a papyrus drew attention of a certain Eratosthenes :
it was about a vertical stick which, on the first day of summer and at noon, did not
cast any shadow on the ground (the Sun's rays reach the bottom of a well!). This
happened very far from Alexandria, straight to the South, in a town called Syene.
However, Eratosthenes noticed from his side that in Alexandria, on June the 21rst
also and at the same time, a stick vertically driven in the ground did cast a shadow,
even if such a shadow was relatively short.
What the hell was this mystery ?
By completing the following Web Quest you will learn about Eratosthenes and how he
managed to measure the circumference of the Earth about 2200 years ago.
To complete the activity you will need to visit a number of web sites or read books and
extract from them various pieces of information.
You are going to write a report from the informations you will collect and from your
observations. This report should be word processed and presented to the class. It is
essential that questions as well as their answers are included in your work.( Diagrams
must also be included ). In your report you will be expected to show all necessary
calculations as well as the final value for the Earth's circumference.
USEFUL WEBSITES
http://www.juliantrubin.com/bigten/eratosthenes.html
http://www.ciese.org/curriculum/noonday/lessons.html
http://isheyevo.ens-lyon.fr/eaae/groupspace/eratosthene/help-for-calculations/angle-of-the-sun/
http://isheyevo.ens-lyon.fr/eaae/groupspace/eratosthene/help-for-calculations/conversion/
http://isheyevo.ens-lyon.fr/eaae/groupspace/eratosthene/help-for-calculations/city/
http://isheyevo.ens-lyon.fr/eaae/groupspace/eratosthene/help-for-calculations/distance/
http://isheyevo.ens-lyon.fr/eaae/groupspace/eratosthene/help-for-calculations/anywhere/

2. Q1) In which city did Eratosthenes live?
Q2) He was a director of one of the great institutions in this city. What was its name?
Q3) What did he read that was of great interest to him?
Q4) When and what evidence convinced people, such as Aristote, that the Earth might be
spherical in shape? Could you imagine an experience to prove it ?
Q5) What experiment did he then carry out? What were the results of this experiment?
Q6) What is the method used by Eratosthene to measure the circumference of the Earth ?
Make a drawing to show how you could repeat his experiment in your school instead of
Alexandria.
Q7) How did Eratosthenes explain the information he had read in the book and the results
of his experiment?
Q8) What other pieces of information did Eratosthenes need to know before he could
calculate the circumference of the Earth ?
Q9) What is the formula used by eratosthene to calculate the earth circumference ?
Q10) Eratosthenes found the distance between Alexandria and Syene by having someone
pace the distance. According to his informations what is the distance between alexandria
and syene ?
Q11) What's the name of Syene today ?
Q12) mark the approximate position of your school and of Syene on a map
Q13) find the vertical distance between your school and Syene (between their respective
lines of latitude). Record this information carefully on the map that you have already used.
Now that you know the distance between your school and Syene and the formula, you
need to determine the central angle. Remember that it was this remarkable association
that Eratosthenes made between Sun angle and central angle that allowed this particular
technique to work. All you need to do is place a vertical stick (shaft) into the ground at your
school and when the sun reaches its highest vertical ascent for the day (solar noon
therefore the shadow length will be the shortest).
Q14) How could you make sure the stick is in a true vertical position ?
Q15) How could you determining the solar noon for your location and time zone ?
Q16) measure the angle of the shadow of the stick. A group of students have done the
experiment last year. They used a 300 mm long stick and measured a shadow of 145 mm
You need to construct a scale diagram showing a your stick rule creating a shadow. The
angle of elevation of the Sun and the Sun angle can then be measured using a protractor.
Use a piece of graph paper for this scale diagram. Make sure that the diagram is very
carefully labelled and has an appropriate title.
Q17) Calulate the circumference of the Earth and the earth radius.
Q18) If the central angle was one degree in error, what effect would this have on the
determination of the circumference?
Q19) What effect 1, 10 or 100 km error in distance measurements between the two cities
have on the calculation of the circumference?
Q20) Compare your results to the theorical one. How could you explain the differences.