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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Journal for History of Mathematics
Journal Basic Information
Journal DOI :
The Korean Society for History of Mathematics
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Volume & Issues
Volume 26, Issue 5_6 - Nov 2013
Volume 26, Issue 4 - Aug 2013
Volume 26, Issue 2_3 - May 2013
Volume 26, Issue 1 - Feb 2013
Selecting the target year
Division Algorithm in SuanXue QiMeng
Hong, Sung Sa ; Hong, Young Hee ; Lee, Seung On ;
Journal for History of Mathematics, volume 26, issue 5_6, 2013, Pages 323~328
DOI : 10.14477/jhm.2013.26.5_6.323
The Division Algorithm is known to be the fundamental foundation for Number Theory and it leads to the Euclidean Algorithm and hence the whole theory of divisibility properties. In JiuZhang SuanShu(九章算術), greatest common divisiors are obtained by the exactly same method as the Euclidean Algorithm in Elements but the other theory on divisibility was not pursued any more in Chinese mathematics. Unlike the other authors of the traditional Chinese mathematics, Zhu ShiJie(朱世傑) noticed in his SuanXue QiMeng(算學啓蒙, 1299) that the Division Algorithm is a really important concept. In , we claimed that Zhu wrote the book with a far more deeper insight on mathematical structures. Investigating the Division Algorithm in SuanXue QiMeng in more detail, we show that his theory of Division Algorithm substantiates his structural apporaches to mathematics.
Indefinite Problem in Wasan
Qu, Anjing ;
Journal for History of Mathematics, volume 26, issue 5_6, 2013, Pages 329~343
DOI : 10.14477/jhm.2013.26.5_6.329
Japanese mathematics, namely Wasan, was well-developed before the Meiji period. Takebe Katahiro (1664-1739) and Nakane Genkei (1662-1733), among a great number of mathematicians in Wasan, maybe the most famous ones. Taking Takebe and Nakane's indefinite problems as examples, the similarities and differences are made between Wasan and Chinese mathematics. According to investigating the sources and attitudes to these problems which both Japanese and Chinese mathematicians dealt with, the paper tries to show how and why Japanese mathematicians accepted Chinese tradition and beyond. As a typical sample of the succession of Chinese tradition, Wasan will help people to understand the real meaning of Chinese tradition deeper.
Looking at HPM through an Old Chestnut: Sum of the Angles of a Triangle
Siu, Man Keung ;
Journal for History of Mathematics, volume 26, issue 5_6, 2013, Pages 345~353
DOI : 10.14477/jhm.2013.26.5_6.345
Some teachers do not regard the computation of the sum of the angles of a triangle by using a cut-and-paste or paper-folding method as providing a proof that the sum of the angles of a triangle is equal to two right angles. Some even think that this way of working is not mathematics but more like an experiment in physics. Some see the method as no better than measurement of the angles by a protractor. The author will examine this issue in the teaching and learning of school geometry and more generally as a specific example from the perspective of HPM (History and Pedagogy of Mathematics).
Harriot's Symbolism and the Theory of Equation
Kye, Young Hee ; Shin, Kyunghee ;
Journal for History of Mathematics, volume 26, issue 5_6, 2013, Pages 355~370
DOI : 10.14477/jhm.2013.26.5_6.355
Thomas Harriot has been introduced in middle school textbooks as a great mathematician who created the sign of inequality. This study is about Harriot's symbolism and the theory of equation. Harriot made symbols of mathematical concepts and operations and used the algebraic visual representation which were combinations of symbols. He also stated solving equations in numbers, canonical, and by reduction. His epoch-making inventions of algebraic equation using notation of operation and letters are similar to recent mathematical representation. This study which reveals Harriot's contribution to general and structural approach of mathematical solution shows many developments of algebra in 16th and 17th centuries from Viete to Harriot and from Harriot to Descartes.
An Assumption on How Archimedes Found out the Center of Gravity of Cones in 《The Method》
Park, Sun-Yong ; Hong, Gap-Ju ;
Journal for History of Mathematics, volume 26, issue 5_6, 2013, Pages 371~388
DOI : 10.14477/jhm.2013.26.5_6.371
, Archimedes presented the famous heuristic technique for calculating areas, volumes and centers of gravity of various plane and solid figures, utilizing the law of the lever. In that treatise, Archimedes used the fact that the center of gravity of a cone lies one-quarter of the way from the center of the base to the vertex, but the proof of this is not extant in his works. This study analyzes the propositions and their relations of
focusing on the procedural characteristics of the 'method' of Archimedes. According to the result of that analysis, this study discusses the likely approach which was taken for Archimedes to find out the center of gravity of a cone.
Reconceptualization of Histo-Genetic Principle
Yoo, Yoon Jae ;
Journal for History of Mathematics, volume 26, issue 5_6, 2013, Pages 389~400
DOI : 10.14477/jhm.2013.26.5_6.389
The article makes a discussion to conceptualize a histo-genetic principle in the real historical view point. The classical histo-genetic principle appeared in 19th century was founded by the recapitulation law suggested by biologist Haeckel, but recently it was shown that the theory on it is no longer true. To establish the alternative rationale, several metaphoric characterizations from the history of mathematics are suggested: among them, problem solving, transition of conceptual knowledge to procedural knowledge, generalization, abstraction, circulation from phenomenon to substance, encapsulation to algebraic representation, change of epistemological view, formation of algorithm, conjecture-proof-refutation, swing between theory and application, and so on.
The Study on the Process of Undergraduate Students' Generating Counter-Examples and Proposing True Statements
Oh, Hye Mi ; Kwon, Oh Nam ;
Journal for History of Mathematics, volume 26, issue 5_6, 2013, Pages 401~416
DOI : 10.14477/jhm.2013.26.5_6.401
There has been increasing interest in recent years in the pedagogical importance of counter-examples that focuses on pedagogical perspectives. But there is no research that undergraduate students' generating counter-examples and proposing the true statements. This study analyze 6 undergraduate students' response to interview tasks and the process of their generating counter-examples and proposing true statements. The results of interviews are that the more undergraduate students generate various counter-examples, the more valid they propose true statements. If undergraduate students have invalid understanding of logical implication and generate only one counter-example, they would not propose true statements that modify the given statement, preserving the antecedent. In pre-service teacher's education and school mathematics class, we need to develop materials and textbooks about counter-examples and false statements.