Which of the following describes the contribution of eratosthenes? discovery of the geocentric theory discovery of a mathematical formula to relate the sides of a right triangle calculation of the circumference of the world to within one percent calculation of the weight of ships by the amount of water they displaced

Eratosthenes (276-194 BC) was a Greek mathematician and astronomer who made an amazingly close calculation of the actual circumference of the earth.  He did it by noting the angle of shadows in two cities during the summer solstice, and then doing geometric calculations that factored in the distance between the cities.  

Oh, and besides math and astronomy, Eratosthenes was also a poet and music theorist, as well as pretty much inventing the field of study we call geography today.  He was what we would call a "polymath" (a person of knowledge of all sorts of things) -- or, what the Greeks called a Πένταθλος (pentathlos).