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The ancient Greek mathematician Hippocrates used similar triangles's theorem to estimate the radius of the earth as 3944.3 miles. What is the specific calculation process?
Process: It happens to be at the zenith of the summer solstice. At the same time, he chose a tall obelisk in Alexandria as a reference and measured the shadow length of the tower from summer to the sun, so that he could measure the angle between the upright obelisk and the sunlight. After obtaining these data, he applied Thales' mathematical law, that is, when a light passes through two parallel lines, their diagonal angles are equal.

Eratosthenes observed that this angle is 7 12', which is equivalent to 1/50 with a circumferential angle of 360. This shows that the arc length corresponding to this angle, that is, the distance from Siena to Alexandria, should be equivalent to 1/50 of the circumference of the earth. Next, with the help of the geodetic data of the Royal Surveyor, Eratosthenes measured the distance between the two cities as 5,000 Greek miles.

Once this result is obtained, the circumference of the earth can be multiplied by 50 and the result is 250,000 Greek miles. In order to conform to the traditional system of dividing the circumference into 60 equal parts, Eratosthenes raised this value to 252,000 Greek so as to be divisible by 60.

The Greek Rio in Egypt is 157.5 meters, which can be converted into modern metric system. The circumference of the earth is about 39,375 kilometers, which is 39,690 kilometers after Eratosthenes's correction, which is surprisingly close to the actual circumference of the earth.

Therefore, Eratosthenes skillfully combined astronomy with geodesy, and accurately measured the precise value of the earth's circumference. This measurement appeared more than 2000 years ago, which is really remarkable and a great achievement in the history of geography.

Mathematical research

Early mathematicians were either rich at home or attached to rich and powerful people who were interested in research. Learning mathematics is more out of hobbies. In modern times, the profession of mathematicians has gradually formed. Their jobs include teaching mathematics courses in schools at all levels, guiding graduate students, conducting research in specific fields, and publishing papers and reports.

Above content reference: Baidu Encyclopedia-Mathematicians