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

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...

• Word Count: 1525
• Approx Pages: 6
• Has Bibliography

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

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). ...

• Word Count: 1993
• Approx Pages: 8
• Has Bibliography