... plane curves (polynomials of degree three in two variables), made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations. He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula) and was the first to use power series with ... development of mathematical analysis. In addition to analysis, Leibniz made a number of important discoveries in other fields of mathematics: combinatorics, algebra (the principles of ...

• Word Count: 6149
• Approx Pages: 25
• Grade Level: Undergraduate

... heavens would be if the Earth truly moved. These assumptions were, of course, based on the works of Aristotle. Galileo wrote to him to correct his errors by using simple geometry (Machamer 29). It is suspected that it was at this point that Galileo began to contemplate the possibilty of heliocentric universe. He admitted in 1597 (albeit only in a private letter ... to solve a large number of geometrical problems (including the extraction of square and cubic roots)? (Fermi 32). The military compass helped navigators, scientists, and many other professionals to do simple geometry. The cre...

• Word Count: 4135
• Approx Pages: 17
• Has Bibliography
• Grade Level: High School