• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.359-367
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• 2009

The graph of the parallelogram law is well known, which gives rise to the characterization of an inner product space among normed linear spaces [6]. In this paper we will sketch graphs of its deformations according to our previous paper [7, Theorem 3.1 and 3.2]; each one of which characterizes an inner product space among normed linear spaces. Consequently, the graphs of some classical characterizations of an inner product space follow easily.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.429-444
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• 2020

For a quadrilateral P, we consider the centroid G0 of the vertices of P, the perimeter centroid G1 of the edges of P and the centroid G2 of the interior of P, respectively. It is well known that P satisfies G0 = G1 or G0 = G2 if and only if it is a parallelogram. In this paper, we investigate various quadrilaterals satisfying G1 = G2. As a result, we establish some characterization theorems. One of them asserts the existence of convex quadrilaterals satisfying G1 = G2 without symmetry.

• School Mathematics
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• v.18 no.3
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• pp.527-539
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• 2016

A word 'is' in "A parallelogram is trapezoid." is ambiguous and very rich when it comes to its meaning. In this paper, 'is' as in everyday language will be identified as semantic primes that can be interpreted in different ways depending on context and situation, and meanings of 'is' in mathematics will be discussed separately. Focusing on 'identity', 'is' will be reinterpreted in the view of equivalence relation and van Hieles' work. 'Is', as a mathematical sign, is thought to have a significant importance in producing mathematical ideas meaningfully.

• Journal of the Korean Society for Precision Engineering
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• v.28 no.7
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• pp.851-858
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• 2011

Nanopositioning technologies play an important role in the progress of electronics, optics, bio-engineering and various nano-scale technologies. As a result, various practical nanopositioning methods have been successfully introduced. Flexure mechanism is a valuable method in nanopositioning because of smooth and friction-free motion and the infinitesimal movement near to sub-nm. In this study a modularized nanopositioner based on parallelogram four-bar linkage structure with right-circular flexure hinge was developed. The positioning performance of a single axis nanopositioner and a XY nanopositioner which was extended from single axis one were demonstrated using control experiments. Consequently, it was shown that the developed single axis nanopositioner possessed high performance and could be extended to various multi-axis nanopositioners.

• Journal of Educational Research in Mathematics
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• v.25 no.3
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• pp.461-472
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• 2015

Korean students are taught area formulas of parallelogram and triangle by inductive reasoning in current curriculum. Inductive thinking is a crucial goal in mathematics education. There are, however, many problems to understand area formula inductively. In this study, those problems are illuminated theoretically and investigated in the class of 5th graders. One way to teach area formulas is suggested by means of process of problem solving with transforming figures.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.247-258
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• 2017

For a quadrilateral P, we consider the centroid $G_0$ of the vertices of P, the perimeter centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. It is well known that P satisfies $G_0=G_1$ or $G_0=G_2$ if and only if it is a parallelogram. In this note, we investigate various quadrilaterals satisfying $G_1=G_2$. As a result, for example, we show that among circumscribed quadrilaterals kites are the only ones satisfying $G_1=G_2$. Furthermore, such kites are completely classified.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.22 no.2
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• pp.185-191
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• 2013

In this paper, the dynamics of a novel 2-DOF planar Translational Parallel Manipulator (TPM) is analyzed. The suggested TPM is made up of two PPa (Prismatic-planar Parallelogram) legs. Since all the linear actuators are mounted on the base, the proposed TPM can be applied for high speed positioning applications. The Lagrangian equations of the first type is employed to derive the inverse dynamic equations. It is shown that the analytical inverse dynamics equations match very well with ADAMS simulations. These analytical inverse dynamics equations will be used for the real-time computed torque control in the further work.

• Journal of the Korean Institute of Telematics and Electronics
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• v.14 no.4
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• pp.15-21
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• 1977

In this paper, an analogical method for measuring the electrical characteristics of the silent discharge in the Na2CO3 electrolyte is proposed by using an electrical equivalent model which consist of charging and discharging circuits. The electrical equivalent model is constructed with the use of zener diode and capacitor, and the electrical characteristics can be obtained by the voltage and charge traces which appear a simple parallelogram on the oscilloscope. The area enclosed by the parallelogram could be considered of the energy input per cycle, and is independent of the applied voltage waveform but dependent on the maximum applied voltage.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.583-592
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• 2002

In this paper, we give Hlawka's type inequalities and related results in n-inner product spaces.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.10a
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• pp.439-440
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• 2009