6. what did eratosthenes invent as a result of his discovery? how did hipparchus, and ptolemy improve his discovery?

Eratosthenes is also called as the father of geography.

Explanation:

On discovery, he invented the discipline of geography as he calculated the surface circumference o the earth and compared the mid angles of the sun from a distance to north and south. His discoveries related to the distance between Alexandria and Syene was 5000 stadia,  Alexandria is due north of Syene and it's on the Tropic of Cancer . That the Earth is a perfect sphere and that the light rays emanating from the Sun are parallel. Hipparchus developed the trigonometry calculations with his solar and lunar theories. He insisted on the measurements for the latitudes and longitudes through the triangulation of the unknown distances. In geographic theory, the methods Hipparchus gave related to the grading grid and geographical latitudes. As the Ptolemy's work is to provide the geographical coordinate and also elected to use the circumference of the earth proposed by rather than the accurate size determined it be 25,000 miles that were close to the Eratosthenes radius of  24,902 miles.

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