Archimedes of Syracuse

287 BC – 212 BC

Even though Archimedes achieved his fame through his mechanical inventions, he believed that pure mathematics was the only worthy pursuit. He is even considered by most mathematical historians as one of the greatest mathematicians of all time. He was able to perfect a method of integration, which allowed him to find areas, volumes, and surface areas of many different bodies. He applied the method of exhaustion to attain a range of important results. He gave an accurate approximation to π and proved to approximate square roots accurately. In fact, in his work Measurement of the Circle, Archimedes showed that the exact value of π lies between 3 10/71 and 3 1/7. He found this by circumscribing and inscribing a circle with regular polygons having 96 sides.

Archimedes was able to discover fundamental principles of mechanics by using methods of geometry. He also discovered fundamental theorems which dealt with the center of gravity of plane figures. For example, he finds the center of gravity of a parallelogram, triangle, and trapezium.

In one of his works, On the Sphere and Cylinder, he showed that the surface area of a sphere is four times that of a great circle. He also finds the area of any segment of a sphere and shows that the volume of a sphere is 2/3 the volume of a circumscribed cylinder.

In another work, On Spirals, Archimedes defines spirals and provides fundamental properties dealing with spirals. He discusses tangents to spirals and investigates the volume of segments of paraboloids, hyperboloids, and spheroids.

In his next work The Sandreckoner, Archimedes proposes a number system capable of expressing a number up to 8 x 10^63 in today’s notation.

Archimedes himself, considered his most significant accomplishments to be those which addressed a cylinder circumscribing a sphere.

References:

Greenberg, Marvin J. Euclidean and Non-Euclidean Geometries:

Development and History. 3rd ed. New York: W.H. Freeman and Company,
1993. 6-19.

Historical Topics for the Mathematics Classroom. Washington D.C.:

National Council of Teachers of Mathematics, 1969.

http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Thales.html (March 2005)

http://geometryalgorithms.com/history.htm (March 2005)

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