The lectures he attended and friendships he developed in GÖttingen would shape Dedekind's future endeavors. ... In 1821, French mathematician Cauchy began to clarify the basis of calculus with his theory of limits, a purely arithmetic theory that did not depend on geometric intuition or infinitesimals. ... The primary motivation behind part one of his book, Continuity and Irrational Numbers, was the desire to replace loose geometrical concepts and intuitive justifications with exact proofs stemming from precisely formulated definitions. ... But the important difference here is that...

• Word Count: 2467
• Approx Pages: 10
• Has Bibliography
• Grade Level: Undergraduate

This theory incorporates the idea that musical sounds have mathematical tones of energy which ultimately allow them to relate with patterns of proportion dealing with angles, shapes, and movements. ... Pythagoras was not one of these men and for this reason he was able to come up with a great change within the geometric division of mathematics. ...

• Word Count: 1076
• Approx Pages: 4
• Grade Level: Undergraduate

HISTORY AND DEVELOPMENT OF CALCULUS Team Number: 6   Name                                                            ID No 1.    DEEPANSHU TIWARI                                 ...

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