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Missing Works Cited

Born the son of an astronomer, Phidias, in 287 B.C., Archimedes' education began as a young man in Syracuse. He furthered his education in Alexandria, where he studied with fellow scholar Conon, an Egyptian mathematician.

What we know of Archimedes comes from his personal works as well as those of Cicero and Plutarch. However, "due to the length of time between Archimedes' death and his biographers' accounts, as well as inconsistencies among their writings, details of his life must remain subject to question" (Galenet 1).

It is doubtless that Archimedes was the greatest geometer of his time, and he has not been paralleled since then. To imagine just how much knowledge he discovered, and the amount of intelligence he must have had to discover it, is practically impossible. "Archimedes' contributions to mathematical knowledge were diverse" (Galenet 1). He discovered the concepts of Pi, the area of a circle, wrote principles on plane/solid geometry, and developed a somewhat rudimentary form of calculus.

In his dealings with plane geometry, Archimedes wrote several treatises, three of which survive today: Measurement of a Circle, Quatdrature of the Parabola, and On Spirals. It is in Measurements of a Circle that Archimedes reveals how he calculated Pi.

Pi was found by using a theoretically simple method. Pi represents the number 3.14... In turn, 3.14 represents the circumference of a circle. In order to find this number, Archimedes started with the obvious: draw a circle.

In this circle, he drew a six-sided polygon, with each vertex touching part of the circle. Similarly, he drew a hexagon on the outside of the circle, with each segment's midpoint touching part of the circle. He calculated the perimeters of both figures. Archimedes then proceeded to double the sides of the polygons, now having two twelve-sided figures, and again found the perimeters. He continued in the fashion of doubling the number of sides of each polygon until he had two ninety-six-sided figures. The perimeter of the inner polygon was 3.1416, and the perimeter of the circumscribed polygon was 3.1527. He used these to values to approximate Pi as being 3.14.

Quadrature of a Parabola was probably Archimedes' basis for creating his legendary "Death Ray". Supposedly, Archimedes developed a ray that was able to focus the sun's energy at a fixed point that was several hundred feet away. Such a concentration of heat and energy would cause the subject to spontaneously combust. How could he have done this?

One version of the story is that Archimedes positioned several enormous mirrors to face the sea. In essence, these mirrors all contributed to form one parabola, the energy of which was aimed at enemy Roman ships. Upon contact with the ships, the Roman fleet burst into flames and was destroyed. Greece successfully sent surviving Roman ships retreating back to their homeland.

Along with the Death Ray, Archimedes created...

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