Application _____________________________________________________________

Of Maths to Science

Made By :-Bal Bharati Public School , Noida

Measuring Earth’s Circumference

Understanding the Concept

Introduction to the topic :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.

About Eratosthenes:

Eratosthenes, a Greek Mathematician, lived in Alexandria, Egypt, in the third century BC.

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).

Eratosthenes

Born 276 BC

Cyrene

Died 194 BC

Alexandria

Ethnicity Greek

Occupation Scholar,

librarian, poet,

and inventor

ObjectiveThe 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.)

ExperimentHe 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

Method: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.

The length of the shadow, the height of the tower and the angle θ, given here in degrees, are related by- tan θ = length of the shadow/height of the tower

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%.

Calculating Earth’s Circumference Mathematically

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.

A Effort made by us to recreate Eratosthenes’ Concept

THANK YOU !!!!!!!!!

Made by :

Dhruv Sharma Devang MehrotraShivangi Gupta Garima Agarwal