• Journal for History of Mathematics
• /
• v.28 no.4
• /
• pp.167-179
• /
• 2015

We study the solution of truncated series of Lee Sang-hyeog with the aspect of visualization. Lee Sang-hyeog solved a problem of truncated series by 4 ways: Shen Kuo' series method, splitting method, difference sequence method, and Ban Chu Cha method. As the structure and solution of truncated series in tertiary number is already clarified with algebraic symbols in some previous research, we express and explain it by visual representation. The explanation and proof of algebraic symbols about truncated series is clear in mathematical aspects; however, it has a lot of difficulties in the aspects of understanding. In other words, it is more effective in the educational situations to provide algebraic symbols after the intuitive understanding of structure and solution of truncated series with visual representation.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.3
• /
• pp.455-462
• /
• 2012

The purpose of this paper is to show that the coset bound can be used to prove the floor bound. Our proof provides a natural relation between the floor bound and the order bound.

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.609-615
• /
• 2022

We give a formula for the sizes of the dual groups. It is obtained by generalizing a size estimation of certain algebraic structure that lies in the heart of the proof of the celebrated primality test by Agrawal, Kayal and Saxena. In turn, by using our formula, we are able to give a streamlined survey of the AKS test.

• The Mathematical Education
• /
• v.48 no.4
• /
• pp.387-398
• /
• 2009

In this paper, we investigated the influence of technology, which gave an impact on students through the process of teaching & learning for the proof of an additive law of sine function in the mathematics education for the gifted. We chose students who were taking a course in enrichment mathematics at Science Education Institute for the Gifted in Mokpo National University, and analyzed their processes of a mathematical inference or conjecture, an algebraic description and a proof by visualization using technology. We found the following facts. That is, the visualization using technology is helpful to the gifted students in understanding principles and concepts of mathematics by intuition. Also, it is helpful to ones verifying various cases and generalizing principles. But, using technology can be a factor that disturbs learning of students who are clumsy with operating technology.

• Journal of the Korean Mathematical Society
• /
• v.41 no.4
• /
• pp.629-646
• /
• 2004

Let G be a compact semialgebraic group and M a semi-algebraic G-set. We prove that there exists a semialgebraic slice at every point of M. Moreover M can be covered by finitely many semialgebraic G-tubes. As an application we give a different proof that every semialgebraic G-set admits a semi algebraic G-embedding into some semialgebraic orthogonal representation space of G, which has been proved in [15].

• Journal for History of Mathematics
• /
• v.17 no.3
• /
• pp.93-108
• /
• 2004

In this article we study on various proofs of the Steiner-Lehmus theorem(any triangle that has two equal angle bisectors is isosceles). We suggest 6 geometric proofs and 3 algebraic proofs of the theorem in detail, analyze these proofs, extract related theorems, proof ideas.

• School Mathematics
• /
• v.10 no.4
• /
• pp.573-581
• /
• 2008

School geometry takes various approaches such as deductive, analytic, and vector methods. Especially, the mathematical connections between these methods are closely related to the mathematical connections between geometry and algebra. This article analysed the geometric consequences of vector algebra from the viewpoint of teacher's subject-matter knowledge and investigated the connections between the geometric proof and the algebraic proof with vector and inner product.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.4
• /
• pp.717-725
• /
• 2009

We show that to every real polynomial of degree n, there corresponds a certain basis for the space of polynomials of degree less than or equal to (n-1). As an application, we give a new proof for the existence and uniqueness of the partial fraction decomposition of a rational function.

• Journal for History of Mathematics
• /
• v.13 no.1
• /
• pp.125-136
• /
• 2000

The notion of MV-algebra was introduced by C.C. Chang in 1958 to provide an algebraic proof of the completeness of Lukasiewicz axioms for infinite valued logic. These algebras appear in the literature under different names: Bricks, Wajsberg algebra, CN-algebra, bounded commutative BCK-algebras, etc. The purpose of this paper is to give a topological lattice completion of semisimple MV-algebras. To this end, we characterize the complete atomic center MV-algebras and semisimple algebras as subalgebras of a cube. Then we define the $\delta$-completion of semisimple MV-algebra and construct the $\delta$-completion. We also study some important properties and extension properties of $\delta$-completion.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.5
• /
• pp.1773-1778
• /
• 2017

We give an alternative proof of a recent result by B. Pasquier stating that for a generalized flag variety X = G/P and an effective ${\mathbb{Q}}-divisor$ D stable with respect to a Borel subgroup the pair (X, D) is Kawamata log terminal if and only if ${\lfloor}D{\rfloor}=0$.