• Journal for History of Mathematics
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• v.21 no.3
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• pp.97-112
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• 2008

In this study, the research results up to now on original word form and its meaning of Korean number words hana, dul, ..., yeol are looked out from math-historically. In fact, finding out original word form and its meaning of hana, dul, and set(ses) may not be possible in the respect of history of mathematics. There might have been a gap between set(ses) and net(nes), and between net(nes) and daseot(daseos). Original word form and its meaning of hana, dul, set(ses), and net(nes) must be found out in different aspect from those of daseot(daseos), yeoseot(yeoseos), ..., yeol. There might have been a gap between yeoseot(yeoseos) and ilgop(ilgob). Coining number word mechanism for ilgop(ilgob), yeodeol,(yeodeolb) and ahop(ahob) might have been same each other. There might have been a gap between ahop(ahob) and yeol. The research results up to now have not paid attention to this gaps sufficiently. But according to history of mathematics, there must have existed several gaps.

• Journal for History of Mathematics
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• v.25 no.2
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• pp.57-70
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• 2012

In this study, a teaching unit for mathematically gifted students is designed, based on Lakatos's perspective. First, students appreciated the exceptions of Desargue theorem and introduced the point at infinity to remove the exceptions. Finally students were guided to realize that the exceptions and the general case of Desargue theorem have equal status. Exploring Desargue theorem with other viewpoints, gifted students experienced the growth of mathematical knowledge due to exceptions of the theorem.

• Journal for History of Mathematics
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• v.26 no.1
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• pp.85-101
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• 2013

This study is to analyse the characteristics of Barrow's theorem on the historical standpoint of hermeneutics and to discuss the teaching-learning sequence for guiding students to reinvent the calculus according to historico-genetic principle. By the historical analysis on the Barrow's theorem, we show the geometric feature of the theorem, conjecture the Barrow's intention in dealing with it, and consider the epistemological obstacles undergone by Barrow. On a basis of this result, we suggest a purposeful and meaning-oriented teaching-learning way for students to realize the sameness of the 'integration' and 'anti-differentiation', and point out the shortcomings and supplement point in current School Mathematic Calculus.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.67-78
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• 2005

In this paper we deals with Leibniz's definition of infinite and infinitely small quantities, infinite quantities and theory of quantified indivisibles in comparison with Galileo's concept of indivisibles. Leibniz developed 'method of indivisible' in order to introduce the integrability of continuous functions. also we deals with this demonstration, with Leibniz's rules of arithmetic of infinitely small and infinite quantities.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.1-8
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• 2005

In this paper, we describe H. Hopf's life and works from the historical point of view. We have a very brief mention of history and results prior to Hopf. He raised the question of the topological implications of the sign of curvature. We discuss his contributions in the field of Riemannian geometry.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.19-38
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• 2008

This study aims to investigate the evolution of calculating the volume of a sphere in eastern and western mathematical history. In western case, Archimedes', Cavalieri's and Kepler's approaches, and in eastern case, Nine Chapters';, Liu Hui's and Zus' approaches are worthy of noting. The common idea of most of these approaches is the infinitesimal concept corresponding to Cavalieri's or Liu-Zu's principle which would developed to the basic idea of Calculus. So this study proposes an alternative to organization of math-textbooks or instructional procedures for teaching the volume of a sphere based on the principle.

• School Mathematics
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• v.9 no.4
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• pp.523-533
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• 2007

This article focused the meaning of Pythagoras' and Euclid's proof about the Pythagorean theorem in a historical and mathematical perspective. Pythagoras' proof using similarity is based on the arithmetic assumption about commensurability. However, Euclid proved the Pythagorean theorem again only using the concept of dissection-rearrangement that is purely geometric so that it does not need commensurability. Pythagoras' and Euclid's different approaches to geometry have to do with Birkhoff's axiom system and Hilbert's axiom system in the school geometry Birkhoff proposed the new axioms for plane geometry accepting real number that is strictly defined. Thus Birkhoff's metrical approach can be defined as a Pythagorean approach that developed geometry based on number. On the other hand, Hilbert succeeded Euclid who had pursued pure geometry that did not depend on number. The difference between the proof using similarity and dissection-rearrangement is related to the unsolved problem in the geometry curriculum that is conflict of Euclid's conventional synthetical approach and modern mathematical approach to geometry.

• Journal for History of Mathematics
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• v.23 no.4
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• pp.1-15
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• 2010

We study the thought of numerical theory of $Sh\grave{a}o$ $K\bar{a}ngji\acute{e}$. He explained the change of universe and everything in his theoretical system in tradition of . It is contained in his . We conjecture that this book influenced . Choi Suk Jung tried to embody the ideas of $Sh\grave{a}o$ $K\bar{a}ngji\acute{e}$ in .

• Journal for History of Mathematics
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• v.19 no.3
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• pp.123-146
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• 2006

The topic in this thesis stems from the current education situation that represses learners' freedom by excessive instruction and compulsory institution, in spite of the education helping learners free from inner prejudice as one of its chief aims. In this thesis, to discuss with an educational aspect, I call the learners' freedom in the learning process 'freedom-in-process' and the learners' freedom as the result of learning 'freedom-as-result'. Through this discussion, the conclusions are as follows; First, learners who enjoy freedom-in-process get to obtain freedom-as-result in mathematics education. Second, freedom-in-process and freedom-as-result appear repeatedly in the process of looking for and gaining structures. Freedom-in-process and freedom-as-result are both faces of coin, like seed and fruit which are related mutually and fertilized each other. For this purpose, Mathematics teacher must have awareness of the value of freedom, cherish the freedom, and enjoy it with his students.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.71-84
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• 2007

J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.