Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
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Analysis of plane figures and their measures in 'GwangmuYangan' from the perspective of Joseon mathematics

조선 산학의 관점에서 <광무양안>에 제시된 평면도형의 측도 분석

  • CHANG Hyewon (Dept. of Math. Edu., Seoul National Univ. of Edu.)
  • 장혜원
  • Received : 2024.04.12
  • Accepted : 2024.04.24
  • Published : 2024.06.30
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Abstract

This study aims to analyze Joseon mathematical knowledge and its application to real world. The mathematical knowledge refers to measuring the area of plane figures, known as square-shaped land(方田). Its application is land surveys(量田) conducted for taxation purposes. Specifically, this study analyzes the correlation between the related contents in representative mathematical books of the Joseon Dynasty, such as MuksaJipsanbub (17th century), Guiljib (18th century), and SanhakIbmun (18th century), and the shapes and areas of plane figures presented in GwangmuYangan (20th century). The analysis reveals both differences and similarities in the measured area between mathematical books and real world land surveys. While most results of the land survey align with the results obtained from mathematical methods, differences arise due to variations in real measurement of lengths and given conditions in the problems. Additionally, various aspects such as the focus on rectangles in land surveys, the proportionality and relativity of lengths, types of approximation, composed shapes, the purpose of problem solving, and reasoning of unspecified shapes or measures are discussed.

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References

  1. CHANG H., Diversity of problem solving methods about a problem of area from the history of mathematics by high achieving elementary school students, The Korean Journal for History of Mathematics 21(4) (2008), 153-168.
  2. CHANG H., Approximate approaches in Chinese and Chosun mathematics, The Korean Journal for History of Mathematics 24(2) (2011), 1-15.
  3. Gyujanggak original text database. https://kyudb.snu.ac.kr/book/view.do 
  4. HONG J., Guiljib, 18c. 홍정하, 구일집, 한국과학기술사자료대계 제2권, 강신원, 장혜원 역, 교우사, 2006.
  5. HWANG Y., SanhakIbmun, 1774. 황윤석, 산학입문, 한국과학기술사자료대계 제3권, 강신원, 장혜원 역, 교우사, 2006.
  6. JO T., JuseoGwangyeon, 1718. 조태구, 주서관견, 한국과학기술사자료대계 제2권.
  7. KIM C., A study on the south upper direction system in cadastral map, Journal of the Korean Society of Cadastre 18(1) (2022), 19-33.
  8. KIM G., A report on the results of the search for a computerization plan of Yangan, 2010.
  9. KIM J., Land survey during the Korean Empire, A report on the results of the search for a computerization plan of Yangan, 2010, 60-92.
  10. KIM S., Characteristics of the Kwangmu land surveys revealed by comparing the Kwangmu Land Registers with the colonical one, Master's thesis in Seoul National University, 2014.
  11. KIM S., Characteristics of the land taxation system in the late Choson dynasty based on the reanalysis of land registers, Doctoral dissertation in Seoul National University, 2021.
  12. KYUNG S., MuksaJibsanbub, 경선징 (17c). 묵사집산법, 한국과학기술사자료대계 제1권, 유인영, 허민 역, 교우사, 2006.
  13. National Institute of the Korean Language, Standard Korean Dictionary, 2023. https://stdict.korean.go.kr/main/main.do 
  14. YANG H., YanghwuiSanbub, 1274. 양휘, 양휘산법, 차종천 역, 교우사, 2006.