Also people say that Euclid of Alexandria is the son of Naucrates, but there is no proof of this assumption. ... The Data, a collection of geometrical theorems; the Phenomena, a description of the heavens; the Optics: the Division of the Scale, a mathematical discussion of music; and several other books have been attributed to him. ... Euclid laid down some of the conventions central to modern mathematical proofs. His book The Elements, written about 300 BC, contains many proofs in the field of geometry and algebra. ... He claims the proof is "remarkably simple". ...

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• Grade Level: High School

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...

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Calculus, which was discovered by Newton and Leibnez some two thousand years later, was anticipated through his studies of the areas and volumes of geometrical shapes, of curved solid figures, and the areas of plane figures. ... A soldier found Archimedes working through a geometrical proof. ... Archimedes wanted to finish his proof and asked to be left alone. ...

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• Grade Level: High School

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...

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• 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". Th...

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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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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...

• Word Count: 818
• Approx Pages: 3

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...

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• Grade Level: Undergraduate

The first group consists of works that have as their major objective the proof of theorems relative to the areas and volumes of figures bounded by curved lines and surfaces. The second category contains works that lead to a geometrical analysis of statical and hydrostatical problems and the use of statics in geometry. ...

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They didn't distinguish numbers from geometrical dots either. ... However, there is a book, which gives 350 proofs on the Pythagorean Theorem. In fact, a United States president proved the theorem, and I have attached his proof to this report. ...

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Although Lonnie Zamora has claimed to see the UFO and the people, he does not have any proof of this, just as Kenneth Arnold doesn't have any proof. ... Crop circles are a design of a very complex geometrical shape that takes place overnight in a crop field. ...

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Absolute perfect circles and geometric shapes have been found where these methods couldn't have made, not matter how hard you try. ... These things are the only few proofs that aliens have ever been to this earth. Yet these are still not solid proof. ...

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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. ...

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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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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. ...

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• 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: 1525
• Approx Pages: 6
• Has Bibliography
• 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. ...

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• Grade Level: Undergraduate

So from the start, the single bullet theory is geometrically impossible. But if you need more proof a weapon found in a room on the sixth story of a library, a 1938 six and a half mille-miter rifle, that would shoot a bullet at a rate of 7.5 feet per second. ...

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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...

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(Toomer, p.p. 190-191) In this work, Ptolemy proposed a geometric theory to account mathematically for the apparent motions and positions of the planets, sun, and moon against a background of unmoving stars. ... In an attempt to support his heliocentric model, Copernicus dedicated years to the mathematical proofs for heliocentric orbits. ...

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Johannes Kepler, was a German born Physicist who was mainly known for his knowledge of planetary orbits. Kepler also contributed numerous works in optics. One of his discoveries was discovering 2 new regular polyhedra. He also gave the first proof of how logarithms worked. Clearly Johannes Kepl...

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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