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 Dedekind applied this concept to numbers, making it solely arithmetical and not geometric, in that the operations on the s...

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

Fractions are used in geometry for understanding geometric equations such as the area of a triangle (A= ½ b*h) and in determining ratios between various geometric objects or shapes. ... As previously mentioned, it is important to meet the students where they are at in terms of geometrical understanding. The van Heile levels break geometric understanding into three levels; 3 levels. ... In these observations, use geometric constructivists activities such as learning centers and mathematics games and manipulatives to reveal the students' van Heile level. ...

• Word Count: 4145
• Approx Pages: 17
• Grade Level: Undergraduate

What about mathematical proofs and geometric theorems? ... He is saying that spiritual people search for miracles from the heavens when there is a definite miracle present in the form of their overwhelming faith in something that has no concrete proof of existence. ...

• Word Count: 1541
• Approx Pages: 6
• Has Bibliography
• Grade Level: Undergraduate

If a species population is to remain constant, environmental pressures from the three sources previously mentioned must balance every species' tendency to increase at a geometric rate. ... For the most part, the struggle for existence and the geometric potential to expand remain balance for long periods of time, but it only requires a small variation to cause drastic changes. ... One can visualize the strength of this balance, by the geometric growth potential; that a single species, if unchecked, could overpopulate the earth in surprisingly few generations. ...

• Word Count: 3127
• Approx Pages: 13
• Has Bibliography
• Grade Level: Undergraduate

HISTORY AND DEVELOPMENT OF CALCULUS Team Number: 6   Name                                                            ID No 1.    DEEPANSHU TIWARI                                 2014A2 PS512H                                                 2. YELLANKI DAKSHAYANI 2014A2PS513H 3. AYUSH UMRAO 2014A2PS515H 4. MANISHA KALLEPALLE 2...

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