... of Alexandria, whose chief work, Elements, is a comprehensive treatise on mathematics in thirteen volumes on such subjects as plane geometry, proportion in general, the properties of numbers, incommensurable magnitudes, and solid geometry. He was probably educated at Athens by pupils of Plato. He taught geometry in Alexandria and founded a school of mathematics there. The Data, a collection of geometrical theorems; the Phenomena, a description of ... original discoveries in the theory of numbers. Euclid laid down some of the conventions central to modern mathematical proofs. His book Th...

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• Grade Level: High School

... , along with Newton and Gauss (10.2. Archimedes shu). He is considered to be the greatest mathematician of antiquity and made his greatest contributions in geometry (Archimedes of Syracuse. math). Archimedes literally invented the study of hydrostatics. In one particular result he was able to compute the maximum angle that ... his work, On Spirals. 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...

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• Has Bibliography
• Grade Level: High School

... too much, though. I was pretty much your basic, well-rounded, A-B student. And I was happy in the comfortable world of understanding. Then I got into high school and it got more complex. Geometry, ok. Makes sense for the most part. Algebra? We're getting into way too many letters and not enough numbers. By the time they got to ... proofs and theorems, I'd been kicked off the "bus of understanding- and was struggling behind on the "bicycle for mathematical delinquents-. To make matters worse, it was at that point that the ... in there. But, as I learned, they want well-rounded teachers...

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• Grade Level: High School

... in his life. One of the most important was Pherekydes. The other two were Thales and his pupil, Anaxmander, both who lived in Miletus. These two philosophers influenced him in geometry and cosmology. Pythagoras was accepted into priesthood at Diospolis in Egypt. It is here where he developed his beliefs which he later imposed on the society that he set up ... lengths of the other two sides. You don't have to be a mathematician to see that this equation is correct, it requires simple reasoning. However, there is a book, which gives 350 proofs on the Pythagorean Theorem. In fact, a United...

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• Grade Level: High School

... heavens would be if the Earth truly moved. These assumptions were, of course, based on the works of Aristotle. Galileo wrote to him to correct his errors by using simple geometry (Machamer 29). It is suspected that it was at this point that Galileo began to contemplate the possibilty of heliocentric universe. He admitted in 1597 (albeit only in a private letter ... falling bodies, his development of the first law of motion and the experiments which led up to it, and his work on the motion of projectiles. There are two major proofs which come out of Galileo's experimentation with falling...

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... Germany and ideas resembled that of Napleon I (2). The French government invited him to explain more details to them. While in Paris he met Huygens which led him to start studying geometry. In 1667, he had written ideas on combinations and also a description of a new calculating machine. "In this work Leibniz aimed to reduce all reasoning and discovery to a combination of basic ... very clumsy and he feared criticism. So he wrote a letter to Leibniz in 1676 which took a great deal of time to reach him. The letter entailed Newton's results, but no proofs of his results. Leibniz realizing...

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• Grade Level: High School

... system. Eratosthenes calculated that the earth's circumference was 24,662 miles and was within 1 percent of our modern calculations. Euclid, a highly regarded mathematician, wrote the elements, which contained 465 geometry propositions and proofs. Another important scientist, Archimedes of Syracuse, accurately estimated the value of pi. He also explained the law of the lever and invented the pulley to lift heavy objects. The ... ...

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• Grade Level: High School

... system. Eratosthenes calculated that the earth's circumference was 24,662 miles and was within 1 percent of our modern calculations. Euclid, a highly regarded mathematician, wrote the Elements, which contained 465 geometry propositions and proofs. Another important scientist, Archimedes of Syracuse, accurately estimated the value of pi. He also explained the law of the lever and invented the pulley to lift heavy objects. The ... ...

• Word Count: 618
• Approx Pages: 2
• Grade Level: High School

... system. Eratosthenes calculated that the earth's circumference was 24,662 miles and was within 1 percent of our modern calculations. Euclid, a highly regarded mathematician, wrote the elements, which contained 465 geometry propositions and proofs. Another important scientist, Archimedes of Syracuse, accurately estimated the value of pi. He also explained the law of the lever and invented the pulley to lift heavy objects. The ... ...

• Word Count: 703
• Approx Pages: 3
• Grade Level: High School

... the need for teachers to be aware of individual learning rates and styles. Van Hieles Dutch educators who taught math for a number of years and discovered students had difficulty understanding geometry. They saw there are five levels a student must past through. 5 levels Visualization Their global appearance and not their property recognize shapes. Analysis Here students observe the component parts of figures ... explain relationships. Informal dedication Here they are able to deduce the properties of figures and express inter relationships, both within and between figures. Formal deduc...

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• Grade Level: High School

... two together. "People who have conducted the Mozart effect experiment have suggested that spatial-temporal reasoning is crucial in math. The areas of math that require spatial-temporal reasoning are geometry and certain aspects of calculus, which require transformations of images in space and time."" (Sommer 3) Although in higher mathematics, "researchers have noticed that the ability to write mathematical ... proofs is also associated with spatial-temporal reasoning."" (Sommer 3) This is said to be true because "proof writing is a task that requires intuitive sense of natural sequences...

• Word Count: 2415
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• Grade Level: High School