2200 years ago (200 B.C.), in the most glorious city of its day, Alexandria in Egypt, was the place where for the first time a man not only made the brave claim of a round and not flat Earth, but also proved it.
The man's name, was Eratosthenes. Why, he wondered did the shadow created by two pillars, in two cities 800 kms (500 miles) away from each other, vary in angles.
The Sun's rays are almost parallel as they hit the Earth, due to its proximity to us.
Therefore he observed, when in Syene, on the longest day of the year (21 June) at noon, the Sun was directly overhead and casted no shadow of the pillar on the ground, at the same time, in Alexandria, the pillar casted a distinct shadow.
He thus came to the conclusion that the Earth must be round. For if the Earth was flat, both the pillars with parallel rays, would cast no shadow at the same time. (Yes, he had hired men to calculate and observe everything)
This man, not only came to the brave conclusion of claiming the Earth round, but also, measured the circumference of this sphere.
His idea was a clever one. (Refer to above picture): The angle formed by the shadow of the Alexandrian pillar, was 7°. The geometric law of parallel lines states, that if a line intersects two || lines, then the opposite angles so formed are equal. Therefore, he imagined a long stick extending from the bottom of the pillar, till the centre of the Earth, where it formed an angle of the same measure as the opposite one.
i.e angle A = angle B = 7°.
Now, the distance between the two pillars was about 800 kms. So Eratosthenes concluded that, if 7° of a sphere was equal to 800 kms, multiplying it into 360° must be the complete length or circumference of the Earth.
His answer was 42,000 kms, which is close enough to the correct measurement of a 45,000 kms.
Eratosthenes is my favourite ancient scientist/mathematician. Who is yours? Please comment. (Picture owned by NASA | Edited/labeled by me)