Changes

Other mathematical principles already understood by the early 2nd millennium BC were concepts of square roots/powers, inverse numbers, quadratic equations, exponential growth, a form of Fourier analysis, and other types of calculation used in geometry and algebra.<ref>For information on Babylonian Fourier analysis, see: Prestini, Elena, and Elena Prestini. 2004. ''The Evolution of Applied Harmonic Analysis''. Boston: Birkhauser. For information on quadratic equations and square roots, see: Kline, Morris. 1972. ''Mathematical Thought from Ancient to Modern Times''. New York: Oxford University Press, pg. 8.</ref> Concepts of zero were also well understood by the early 2nd millennium and were represented as a space or symbol in Mesopotamia and Egypt respective.<ref>For a history of zero, see: Bunt, Lucas N. H., Phillip S. Jones, and Jack D. Bedient. 1988. ''The Historical Roots of Elementary Mathematics''. New York: Dover Publications.</ref> Very recently, a paper was published that showed the Babylonians had already developed an early forerunner of calculus, by around 2000 BC using abstract mathematics for estimating distances plants travel in space. Previously, some of the forms of Mesopotamian calculations used for complex shapes and distances were assumed not to have been invented until the 14th century AD.<ref>For this paper, see: Ossendrijver, M. 2016. “Ancient Babylonian Astronomers Calculated Jupiters Position from the Area under a Time-Velocity Graph.” ''Science 351'' (6272): 482–84. doi:10.1126/science.aad8085.</ref>

==The Role of Astronomy==