1. _____________________________________________________________
Of Maths to Science
Measuring Earth’s Circumference
Made By :Bal Bharati Public School
, Noida

2. Understanding the Concept

3. Around
250 BC, at noon on the day of
the summer solstice in
Syene, Egypt, Eratosthenes observed that
sunlight filled the vertical shaft of a well.
Eratosthenes,
heard of this from a traveler
and on the same day, different year, he
observed that in Alexandria, the vertical
pole cast a shadow and from these
observations, he made two deductions:
A. the earth is curved;
B. found the first estimate for the
circumference of the Earth.

4. Eratosthenes
Eratosthenes,
a Greek Mathematician,
lived in Alexandria, Egypt, in the third
century BC.
Born
276 BC
Cyrene
Died
194 BC
Alexandria
Ethnicity
Greek
Occupation
Scholar, librarian,
poet, and
inventor
He
was the first person to calculate
the circumference of the earth by using a
measuring system - Stades.
He was the first one to calculate the tilt
of the earth’s axis(also with remarkable
accuracy).


5. The goal of this project is to
estimate the circumference
of the earth by setting up a
mathematical proportion from
simple measurements.
(To be exact, the
Circumference of the earth as
measured by modern-day
equipments is estimate.)

6. He measured the angle of a shadow in Alexandria at noon on the
same day, the angle of the shadow would be the same as the central
angle of the "wedge" of the Earth between Alexandria and Syene.
CONCEPTS USED- The various
concepts used while
preparing the project were:-
1) Application of Trigonometry
in Daily Life
2) Longitudes and Latitudes

7. Imagine
the earth cut in half
along the north-south line between
Alexandria and Syene, and then
looking at the cut section, face-on
(blue circle).
Since
there are 360 degrees in a
circle, by dividing the central angle
into 360, he could calculate how
many similar sectors would be needed
to complete a circle.

8. The
length of the shadow, the height of the tower and the
angle θ, given here in degrees, are related bytan θ = length of the shadow/height of the tower

9. Using this method developed about 2,200 years ago,
Eratosthenes, was able to roughly estimate the circumference
of the Earth. His measurement turned out to be 39,690 km, an
error of 1.6%.

10. 
A denotes the base of the pole in
Alexandria;
S the base of a pole in Syrene;
T the tip of the shadow cast by the
pole in Alexandria;
P the top of the same pole;
E the center of the Earth.
The
distance from Alexandria to Syrene is 800 km, so he concluded
that the circumference of the Earth must be 51.4*800=41120 km
This
estimate is very close to modern accurate measurements, so
Eratosthenes gets credit for the first calculation of the size of the Earth.

12. Made by :
Dhruv Sharma
Shivangi Gupta
Devang Mehrotra
Garima Agarwal