300 BC

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Authors: Sergio Gonzalez, Clarence L. Terry, Charles DeBoer, Henry Sheen

Aristarchus was only 10 this year. He was later to find an improved value for the length of the length of the solar year. Nicomedes was brought into the world this year. He died 60 years later.
Autolycus of Pitane and Perseus was born. Sun Zi, also known as Master Sun may have been alive in this year. Little is known about the author of the famous Chinese mathematical text Sun Tze Suan Ching. This book "provides its readers with a valuable source for understanding the rod numerals computation process and the famous Chinese remainder problem.

Author: Sergio Gonzalez

References:
Mactutor Website, http://www-groups.dcs.st-andrews.ac.uk/~history/Chronology/WhoWasThere.html

History of Mathematics! Website, http://mathserv.math.sfu.ca/History_of_Math/mapidx.html

Approximately during the year 300 B.C. was the time when Euclid produced his famous work Elements, not to be confused with the work of Hippocrates under the same title. Euclid's elements was a comprehensive work in the areas of geometry, proportions, and the theory of numbers. Euclid, a disciple of the Platonic school, produced this 13-volume work that is considered
to be "the most long-lived of all mathematical works." (Web Reference) Euclid's approach to geometry has dominated the teaching of the subject for over two-thousand years and Marvin Greenberg (author of `Euclidean and non-Euclidean Geometries: Development and History) consider Euclid to be the most widely-read author in the history of mankind. Greenberg goes on to state
that "the axiomatic method used by Euclid is the prototype for all of what we now call 'pure mathematics.'" Euclid, a Greek mathematician is responsible for the origin of geometry as the vast majority of those who encounter mathematics know it.

Author: Clarence L. Terry

References:
http://ncsa.uiuc.edu/SDG/Experimental/vatican.exhibit/d-mathematics/Greek_math.html

Greenberg, Marvin Jay. `Euclidean and non-Euclidean Geometries: Development and History (Third Edition). W.H. Freeman and Company. New York, 1993.

Euclid writes thirteen books called The Elements which contain the foundations of Greek geometry and number theory. His work contains two centuries of development.

Chinese have a numeration system similar to ours.

Archimedes writes many books including "Elements of Mechanics" and "On Spirals."

Author: Charles DeBoer

References:
"Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences", vol 1, ed. Gratten-Guinness, Routledge, London, 1994

Perfect Numbers

Perfect numbers are numbers where of their factors except themselves add up to itself. For example, 6 is a perfect number because its factors are 1,2,3 and 6. If 1, 2, 3 are added, then 1+2+3 = 6 is obtained. A formula for finding perfect numbers consists of starting with the number 2. The number 2 is doubled (22 = 4). If one less than this result is prime (4-1 = 3), then the prime number is multiplied with the number which was doubled. In this case, 3 and 2 are multiplied to create 6, a perfect number. To continue, the number 4 is doubled. Since 4 times 2 is 8 and 8-1 is prime, 7 and 4 are multiplied to obtain 28, the next perfect number. This process is continued to find consecutive perfect numbers.

It is not known when perfect numbers were first studied, however, anthropological studies indicate that they probably go back to ancient times when human beings were experimenting with numbers. Pythagoras was the first person in recorded history to have studied perfect numbers. Although Pythagoras and his students studied perfect numbers, they were more interested in their "mystical powers" than in the mathematical concepts involved.

The first recorded mathematical result concerning perfect numbers occurs in Euclid's Elements, written around 300 B.C. In his book Euclid states, "If as many numbers as we please beginning from a unit be set out continuously in double proportion, until the sum of all becomes a prime, and if the sum multiplied into the last make some number, the product will be perfect." Euclid's proof which provided the first significant result on perfect numbers is as follows:

1 + 2 + 4 + … + 2^(k-1) = 2^k - 1

If for some k > 1, 2^k - 1 is prime, then 2^(k-1)(2^k -1 ) is a perfect number.

Continuous studies on perfect numbers by various mathematicians has lead to 35 known primes and their corresponding perfect numbers. However, no one has found an odd perfect number. Whether or not there are any odd perfect numbers is the oldest unsolved problem in mathematics.

Author: Henry Sheen

References:
Hall, H.S. A textbook of Euclid's Elements for the use of schools. London: MacMillan 1902.

http://www.sps-zr.hiedu.cz/jez/perfect2.html

Last updated December 1998