Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
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A generalization of Yeonhwando in Yang Hui Suanfa

양휘산법 (楊輝算法) 에 제시된 연환도 (連環圖) 의 일반화

  • Park, Kyo Sik (Dept. of Math. Edu. Gyeongin National Univ. of Edu.)
  • Received : 2016.07.13
  • Accepted : 2016.08.26
  • Published : 2016.08.31
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Abstract

In this paper, the problem posed in Yeonhwando is presumed like the following: "Make the sum of eight numbers in each 13 octagons to be 292, and the sum of four numbers in each 12 squares to be 146 using every numbers once from 1 to 72." Regarding this problem, in this paper, firstly, it is commented that there can be a lot of derived solutions from the Yang Hui's solution. Secondly, the Yang Hui's solution is generalized by using sequence 1 in which the sum of neighbouring two numbers are 73, 73-x by turns, and sequence 2 in which the sum of neighbouring two numbers are 73, 73+x by turns. Thirdly, the Yang Hui's solution is generalized by using the alternating method.

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References

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