Regarding the shape of the earth, ancient Greek scholars have several different views: some people think it is flat, disc-shaped or rectangular; But there are also many people who correctly think it is a sphere, because they judge that the circular shadow on the moon during the eclipse is the projection of the earth. Eratostheny, a famous mathematician who was then the curator of Alexandria Library, first tried to calculate the circumference of the earth with strict mathematical methods.
Eratosthenes learned that at noon every summer solstice, the sun shines directly at the bottom of a deep well in Thain (now Aswan, Egypt); Meanwhile, in Alexandria, about 5,000 Greek miles north of Thain, the angle between the sunlight and the vertical line on the ground is 2π/50 radians (7.2). Assuming that the sunlight is parallel, according to the formula for calculating the circumference, the circumference of the earth along the meridian passing through the north and south poles is
Perimeter = 5000×2π÷2π/50? = 250,000 Greek miles.
According to the length unit of Athens, 1 Greek is equal to 185 meters, from which the circumference of the earth is calculated to be more than 46,000 kilometers. According to the Egyptian unit of length, 1 Greek mile is equal to 157.5 meters, and the circumference of the earth is about 39,000 kilometers.
Now people have accurately measured that the meridian circumference of the earth is 40 008 kilometers. It can be seen that Eratosthenes's calculation more than 2,000 years ago is relatively accurate.
Another important mathematical contribution of Eratosthenes is that he invented an effective method for screening prime numbers-later called "Eratosthenes screening method".