Calculus
From Panther Academy
By Ana Areiza, Shafi Ahsanul, Romeris Rosario and Kendrick Nunez
Apply Eratosthenes Measurements between Paterson, NJ, USA and Kuantan, Malaysia.
Students at PANTHER Academy have used the trigonometric method with the shadow length to measure
the circumference of the earth. They came up with very accurate results. Students interacted with various
cities and schools around the world in Malaysia, USA and France. The project was a great success.
T he dista nce bet ween
Pat erso n and Kuat an
The Sun
is 4130 Km.
Paterson
The Earth
Kuantan
Stick
Time
Casted
City
Latitude
Longitude
Shadow`s
Angular
Latitudes
The earth
Height
Shadow
Length
Angle
Separation
Distance
circumference
Paterson
New Jersey
40.9169N
74.1725W
77.4 cm
USA
100 cm
12:30
37.70
37.170
4130 Km.
39997.2 km
PM
Kuantan,
Pahang
3.81N
103.33E
101cm
01 cm
0.560
Malaysia
The circumference of earth =
The circumference of earth=
= 39997.2 km
r =
= 6365.75 km
Such as, x1= shadow length in Paterson, x2= shadow length in Kuantan, L= the Length of the ruler stick (100 cm),
is the shadow angle in Paterson,
is the shadow angle in Kuantan.
= is the angular separation between Paterson and Kuantan.
r= is the radius of the earth, C= is the circumference of the earth.
After communicating with a group of students in Malaysia. Students have col ected information about latitude and
gratitude in addition to their shadow angle. Students went out of the classroom to measure Paterson`s sun shadow.
After shadow`s measurement in Paterson, USA our students have concluded the result that the circumference of earth
is about 39997.2 km which is close to NASA`s information 40,705 km.
Students have learned how to apply pre-calculus and calculus to our real life situation.
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