With a simple angle dangle meter we could measure how big is the earth. We did this by measuring the angle made by Dhruva tara with the horizon from two different places like Simla and Mumbai. We get two different results, because as you move north the angle increases. If you move north by 500 kilometres, the angle increases by around 4.5 degrees. Going around the earth you would traverse 360 degrees of latitude. By ratio and proportion you can work out that the circumference of the earth is around 40,000 kilometres.
By the end of sixth class we learn about triangles, angles, and ratio and proportion. We know how to measure angles with a protractor and distances with a scale. We begin to learn geometry. The word geometry comes from “measuring land”, and our ancient forefathers developed this understanding from measuring things while building structures.
We know from history that in the third century BC (more than 200 years B.C.) a Greek scientist named Eratosthenes first measured the radius of the earth and obtained an answer of around 6400 kilometres. He used a different method than ours, working with shadows cast by an upright rod at noon at different points of the earth . To go from measuring buildings and land to measuring the whole earth required a daring leap of the mind. All great discoveries are made by making a daring leap of the mind from things that we know. Measuring the size of the earth is one of the ten most important experiments in human history.
What is most interesting to know is that Eratosthenes was not the first person to do the noon shadow experiment and obtain the answer of 6400 kilometres. This experiment was first done two hundred years before Eratosthenes by the Greek scientist Anaxagorus, who made an even more daring leap of the mind. To understand his brilliant idea, consider the following experiment.
Suppose you and a friend are going for a walk at night. You see a tall streetlight. You stand directly underneath the streetlight, while your friend stands about 10 metres away. If you examine your shadows you will find that your shadow is small, while your friend’s shadow is bigger. By measuring the length of your friends shadow you should be able to figure out the height of the street lamp from the ground. Can you do it ? Draw a diagram and think about how to do it.
All you need to do is to use some graph paper and what you know about angles, lengths and ratios. Basically, you will have to find out the ratio of the length of your friends shadow to the distance between the end of the shadow and the streetlight base. This is equal to the ratio of your friend’s height to the height of the streetlamp above the ground. It’s the same idea of finding the height of a building without climbing it.
Anaxagorus knew that when the shadow of a pole was of zero length in Alexandria, it was not zero at Syene. He knew the distance between Alexandria and Syene. He thought , “the Sun is just a very high streetlamp”, and calculated the height of the Sun as 6400 kilometres by the same method which we have just discussed in the previous paragraph. It was the right answer, which Anaxagorus obtained 200years before Eratosthenes. But it was not the right answer to the question that Anaxagorus was asking- the question “How far is the sun from the earth?”. It was the right answer to a completely different question.
Anaxagorus did not know that the earth was round like a globe. He assumed that the earth was flat. He had obtained the right answer to the question “ What is the radius of the earth”, but this was not the question that he had asked, because he did not know that the earth had a radius. His geometry, his measurements, his calculations, his numerical answer were all correct. But it was a wrong answer to his question, because of one wrong assumption- the assumption that the earth was flat.
At that time nobody knew that the earth was round. When Anaxagorus declared that the sun was 6400 kilometres away, he was asked to take back his claim and apologize, because his claim went against the prevailing religious beliefs. He was so sure of his calculations that he refused to withdraw his claim, another act of great daring and courage. For his stubbornness he had to pay the price of being banished from his community.
Anaxagorus was not only a great scientist, but also a great intellectual hero, like Giordano Bruno many centuries later who refused to take back his statements that the earth went round the sun, and that the stars were only distant suns. Bruno was burned alive by the Church authorities. There are not many persons who have the courage to stand by their convictions come what may. It is these outstanding individuals who, like Bhagat Singh from our recent history, or like Eklavya, Charvaka and Shambuka from our ancient myths , are the true heroes of all humanity.