- 소인수분해정리와 유클리드의 원론
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- Journal for History of Mathematics, volume 17, issue 1, 2004, Pages 33~42
Abstract
In this paper, we identify the essential ideas of Fundamental Theorem of Arithmetic(FTA). Then, we compare these ideas with several theorems of Euclid's Elements to investigate whether the essential ideas of FTA are contained in Elements or not. From this, we have the following conclusion: Even though Elements doesn't contain FTA explicitly, it contains all of the essential ideas of FTA. Finally, we assert two reasons why Greeks couldn't mention FTA explicitly. First, they oriented geometrically, and so they understood the concept of 'divide' as 'metric'. So they might have difficulty to find the divisor of the given number and the divisor of the divisor continuously. Second, they have limit to use notation in Mathematics. So they couldn't represent the given composite number as multiplication of all of its prime divisors.