1. Earth’s circumference

2. Eratosthenes He invented a system of latitude and longitude.
He was the first to calculate the tilt of the Earth's axis
He also created the first map of the world incorporating parallels and meridians
He was the first person to calculate the circumference of the earth
Eratosthenes of Cyrene was a Greek mathematician, geographer , poet, athlete, astronomer, and music theorist.

3. History
Eratosthenes calculated the circumference of the Earth without leaving Egypt. Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Swenet on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the sun was 1/50th of a circle (7°12') south of the zenith on the solstice noon. He find out that a circumference is about of 46,620 km, i.e. 16.3% too large.

4. Purpose
Find the circumference of the Earth without using modern inventions
Verify Eratosthenes's theory.

5. Hypothesis
I think that my results will differ from real results.

6. Materials
Stick
Sun
Ruler
Calculator
Friends abroad 

7. Process
Our school and others schools (from project LULATS) measure shadows in daylight.
We send each other results
We chose Spain’s results.

8. What we need? C C - Earth’s circumferencez1 z2
Tauragė L y
C - Earth’s circumference
L – distance between Taurage and Madrid
Y – angle
z1 z2 – the angles of elevation of the sun
Madrid

9. Formulas z1 z2 y

10. How find the angle of elevation of the sun?
We need a stick
Stick’s shadow at noon
An angle between a stick and its shadows

11. Our results Stick length Shadow lelngth 139 cm 98 cm 140cm 98,5 cm

12. Our Angle a(average) = z1 = 53.67° b= 36.33° a = 54.81° a = 54.87°

13. Madrid Results Stick’s length – 100cm Shadow’s length – 40.5 cm
Spain time 12:00 13:00 14:00 14:13
Solar time 10:00 11:00 12:00 12:13
length 70,50 51,00 40,50 39,00
Stick’s length – 100cm
Shadow’s length – 40.5 cm
Angle 22.04°
Madrid is in a different geographic longitude. So we need to add two hours and then we will get right result.

14. Distance between Madrid and Taurage
H = 7.95 cm
L= 200*7.95= 1590 km

15. Calculating…
L = 1590km
z1 = 36.33°
z2 = 22.04°

16. Radius R
Rreal= 6378,137km

17. Why don’t we use just a map?
55.15°
y = ° ° = 14.91°
40.24°

18. Calculating…

19. Radius R
Rreal= 6378,137km

20. Results Name With shadows With a map Real results Angle 14.29° 14.91°
Earth’s circumference km km
Radius km
6113.1km
6378,137km

21. Findings Eratosthenes's theory has been reasserted.
We got almost the same result without leaving Taurage
We can easily find Earth’s circumference, when we know two different cities’ geographic latitudes.

22. Thank you for your attention