• Journal for History of Mathematics
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• v.32 no.6
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• pp.259-270
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• 2019

Haidao Suanjing was introduced into Joseon by discussion in Yang Hui Suanfa (楊輝算法) which was brought into Joseon in the 15th century. As is well known, the basic mathematical structure of Haidao Suanjing is perfectly illustrated in Yang Hui Suanfa. Since the 17th century, Chinese mathematicians understood the haidao problem by the Western mathematics, namely an application of similar triangles. The purpose of our paper is to investigate the history of the haidao problem in the Joseon Dynasty. The Joseon mathematicians mainly conformed to Yang Hui's verifications. As a result of the influx of the Western mathematics of the Qing dynasty for the study of astronomy in the 18th century Joseon, Joseon mathematicians also accepted the Western approach to the problem along with Yang Hui Suanfa.

• Journal for History of Mathematics
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• v.29 no.4
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• pp.219-232
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• 2016

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.

• Journal for History of Mathematics
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• v.27 no.1
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• pp.1-12
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• 2014

From the mid 17th century, Joseon mathematics had a new beginning and developed along two directions, namely the traditional mathematics and one influenced by western mathematics. A great Joseon mathematician if not the greatest, Hong JeongHa was able to complete the Song-Yuan mathematics in his book GuIlJib based on his studies of merely Suanxue Qimeng, YangHui Suanfa and Suanfa Tongzong. Although Hong JeongHa did not deal with the systems of equations of higher degrees and general systems of linear congruences, he had the more advanced theories of right triangles and equations together with the number theory. The purpose of this paper is to show that Hong was able to realize the completion through his perfect understanding of mathematical structures.