Hipprocrates never really fully solved the problem of doubling the cube and other mathematicians tried to develop other solutions to the geometric puzzle. ... Since Eudemus seemed satisfied that Hippocrates had proof of his theory, we almost can conclude that Hippocrates himself developed at least a part of the method of exhaustion. Much of Hippocrate's work is difficult to prove such as he was the first to use geometric figures and that he established the technical meaning of the word "power" which is used in algebra today. Hippocrates" other contributions to math were geomet...

• Word Count: 1099
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He was often so into his geometry that his servants would force him to get into a bathtub and, even while his servants anointed him with oils and perfumes, he would try to draw geometric diagrams on his body in the oil on his skin. ... The method is basically a "geometric method of the lever." ... He tells how he was in the habit of sending them statements of his latest theorems, but without giving proofs. Some of the mathematicians there had claimed the results as their own, so Archimedes says that on the last occasion when he sent them theorems, he included two, which were false: so tha...

• Word Count: 1479
• Approx Pages: 6
• Has Bibliography
• Grade Level: High School

Cultural Background Claudius Ptolemy was born about 85 A.D. in Egypt and died about 165 A.D. in Alexandria, Egypt. He did his major works in Alexandria, which was the center of Greek learning. His name Claudius Ptolemy, is a mixture of the Greek Egyptian "Ptolemy" and the Roman "Claudius". This...

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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

He devised and constructed a geometrical and military compass, and wrote a handbook which describes how to use this instrument. ... He was able to do this buy using a new form of math at the time known to us as algebra, which gave him the ability to take simple math problems and make them almost as complex as geometrical equations. ... This is proof that people look to Galileo's work for - 5 - inspiration, and to help with there own work and theories. ...

• Word Count: 1527
• Approx Pages: 6
• Grade Level: High School

Oral instructions were given in geometric terms. ... Patience, precision, "don't give up-, creativity, geometric concepts, and that math class is fun. ... Topics taught in this way range across the entire curriculum: problem solving; precise use of mathematical terminology; ratios, fractions, and percents; angles; area and volume; congruence; tessellations; combinatorics; properties of parallel lines; products and factors; conic sections; Euler's formula; logic; proofs; even concepts from calculus such as tangent line approximations to curves or negative curvature in a hyperbolic par...

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• Has Bibliography

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

In the third century B.C., Archimedes of Syracuse created a special spiral-shaped curve by pulling the legs of a compass apart while turning it. By performing both actions at a steady rate, he found that the resulting  spiral  moved outward by the same amount with each turn of the compass. The gr...

• Word Count: 1264
• Approx Pages: 5
• Grade Level: High School

Euclid is considered the father of geometry, and reorganized a compilation of geometry proofs and created the most successful math textbook. ... They stamped geometric designs of gods, heroes, and other portraits on the gold, silver, or bronze coins. ...

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because of his constant questioning and arguing against anything his professors said that could not be backed up by solid proof? ... Even as a student, he could not tolerate superstition or claims not backed up by proof, preferably mathematical (Levinger 8). ... Unlike his predecessors, he had proof to back up his claims. ... He admitted in 1597 (albeit only in a private letter to his German contemporary Johannes Kepler) to his belief in the Copernican doctrine, but said that he would not come forward with his views because he had no proof, and was afraid of ridicule in the scientific co...

• Word Count: 4135
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• Grade Level: High School

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

He mainly focused on the motion of the sun, planets and moon and uses geometrical models. ... Thus through his premise he argued that the act of thinking offers a proof that individual exists. ... In addition, people started doubting the existence of God as there was no scientific proof to show that he exists, people then chose to form other religions or become atheist (McGrath, 2004). ...

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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

Final Examination 1. Heraclitus makes the statement that "you can't step into the same river twice." This comes from the idea that the river is flowing and ever changing. With its constant flow, by the time you put your foot in take it out and put it back in again, the water you first touched wi...

• Word Count: 4182
• Approx Pages: 17
• Grade Level: High School

Northern Caribbean University College of Education and Religion Department of Education MTED 201: Primary Mathematics Methods Factors that influence how children learn Psychological influences Professional influences Technological influences Language influences Societal influences ...

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• Grade Level: High School

Rhetoricians, and most notably the Sophists, were believers in nomos. Philosophers, for example Plato, were believers in Physis. Nomos is loosely translated as LAW; while PHYSIS is loosely translated as nature. Those who believed in NOMOS argued that reality, and therefore human understanding of that reality, was a product of human action. In other words, what we thought of as real and true were basically the products of our own thoughts and actions--our communication. ...

• Word Count: 3636
• Approx Pages: 15
• Has Bibliography
• Grade Level: High School