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:
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)