1. CIRCUMFERENCE OF THE EARTH

2. In the third century BC, the Greek mathematician Eratosthenes
was asked to find the circumference of the earth.

4. He knew that the rays of the sun fall to earth in
parallel lines.

5. He knew that when parallel lines
are cut by a transversal
alternate interior angles
have the same measure

6. He knew that if he went to the city of syene at noon on June 19

7. He knew that if he went to the city of syene at noon on June 19
he would see light shining out of the famous well.

8. WELCOME TO SYENE
HOME OF FAMOUS WELL

11. The sunlight reflects
only if the sun is
directly overhead!

12. The rays of the sun are
perpendicular to the
earth at this point

13. I know the distance between Syene and Alexandia.
On June 19 I will be in Alexandria.
There I will erect a flagpole

14. flagpole at Alexandria
well at Syene

15. The measure of this angle is 1/50 of a circle

19. 1/50 of a circle
1/50 of a circle

20. Fifty times the distance between Syene and
Alexandia is the circumference of
the earth!