Answer:
In "The Sand Reckoner," Archimedes realizes that the number of grains of sand that can fit inside the universe is not infinite. This realization turns the story toward its resolution because it allows Archimedes to make progress in his attempt to measure the size of the universe.
Archimedes had been tasked by King Hieron of Syracuse with finding a way to measure the size of the universe. He had been struggling with this problem for some time, but his breakthrough came when he realized that the number of grains of sand that can fit inside the Great Harbor of Syracuse, which he knew to be a finite space, could be used to represent a limit on the number of grains of sand that could fit inside the universe.
By calculating the volume of the Great Harbor and estimating the number of grains of sand that could fit inside it, Archimedes was able to make progress in his attempt to measure the size of the universe. Although he did not arrive at a precise answer, his work in "The Sand Reckoner" laid the foundation for future developments in astronomy and physics, and it established Archimedes as one of the greatest mathematicians and scientists of all time