Earth’s circumference
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.
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.
Purpose
• Find the circumference of the Earth without
using modern inventions
• Verify Eratosthenes's theory.
Hypothesis
• I think that my results will differ from real
results.
Materials
•
•
•
•
•
Stick
Sun
Ruler
Calculator
Friends abroad 
Process
• Our school and others schools (from project
LULATS) measure shadows in daylight.
• We send each other results
• We chose Spain’s results.
What we need?
C
z1
Tauragė
L
y
Madrid
z2
• C - Earth’s circumference
• L – distance between
Taurage and Madrid
• Y – angle
• z1 z2 – the angles of
elevation of the sun
Formulas
z1
z2
y
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
Our results
Stick length
• 139 cm
• 140cm
• 127 cm
• 133 cm
Shadow lelngth
•
•
•
•
98 cm
98,5 cm
92 cm
108 cm
Our Angle
a
a
a
a
= 54.81°
= 54.87°
= 54.08°
= 50.92 °
b
a(average) = z1 = 53.67°
b= 36.33°
a
Madrid Results
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.
Distance between Madrid and Taurage
H = 7.95 cm
L= 200*7.95= 1590 km
Calculating…
L = 1590km
z1 = 36.33°
z2 = 22.04°
Radius
R
Rreal= 6378,137km
Why don’t we use just a map?
55.15°
y = 55.15° - 40.24° = 14.91°
40.24°
Calculating…
Radius
R
Rreal= 6378,137km
Results
Name
With shadows
With a map
Angle
14.29°
14.91°
Earth’s
circumference
40055.98km
38390.38km
Radius
6378.34km
6113.1km
Real results
6378,137km
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.
Thank you for your attention