• Journal of the Korean Society of Fashion and Beauty
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• v.4 no.1 s.7
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• pp.28-34
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• 2006

The purpose of this study is to historically examine the thoughts and ideas of geometry and to analyze the expression style of design applied to the mass communication such as magazines and world wide webs, by giving definitions on the ideas of geometry and the pattern of cognition. Geometry was evolved to Descartes's analytical geometry, projective geometry, non-Euclidean geometry and Topology at the end of 19th century. When geometry applies to design styles, it is devided into two field, plane geometry and solid geometry. The development of geometry was completed from the Pythagoras symbolic theory of number to Platonic spiritual geometry and Euclidean geometry. It can be studied that those have what kind of symbolic meanings and transformations on each hair design plan. It can also analized how those symbolic forms are appeared on the design form. This tendency means that there is always a try for the use of geometry as reasonable device for hair design. If the hair design and geometry have logical and artistical relation, we can make buildings which have a order, balance and harmony.

• Journal of the Korean Home Economics Association
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• v.47 no.4
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• pp.61-72
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• 2009

The purpose of this research is to suggest a new way to approach measuring the waist line of slacks. The pattern formulated enables a construction method that optimizes motion. The method is based on the measurement on the length change of the body surface line. The research reveals: 1. The analysis of expansion and contraction by area showed that G8 markedly shrunk, whilst G15 maximally stretched during M4 motion. 2. The areas that stretched during M2 motion were, in order of size: G10, G17, G16, and G8. Conversely, the areas that shrunk are, in order, G9, G11, and G18. The areas that stretched during M3 motion were G10, G17, G16, G12, and G15; the areas that shrunk were G9, G11, G18, and G8. 3. In constructing the slacks pattern to allow for appropriate movement, we calculated the length between the knee and back of the waist, point (y), using Pythagoras’theorem and trigonometry. The equation was y = 1.005x. 4. In the two pattern N method and L method, y is equal or less than x, but for our research pattern, y was larger than x

• Journal for History of Mathematics
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• v.19 no.4
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• pp.81-96
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• 2006

This paper aims to review Leibniz's analytic ideas in his philosophy, logics, and mathematics. History of analysis in mathematics ascend its origin to Greek period. Analysis was used to prove geometrical theorems since Pythagoras. Pappus took foundation in analysis more systematically. Descartes tried to find the value of analysis as a heuristics and found analytic geometry. And Descartes and Leibniz thought that analysis was played most important role in investigating studies and inventing new truths including mathematics. Among these discussions about analysis, this paper investigate Leibniz's analysis focusing to his ideas over the whole of his studies.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.529-546
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• 2010

This study aims to analyze and criticize the definition of the similarity concept in mathematical texts by investigating mathematical history. At first, we analyzed the definition of Pythagoras, the definition of Euclid's ${\ll}$Elements${\gg}$, the definition of Clairaut's ${\ll}$Elements of geometry${\gg}$, the postulate of Brkhoff's postulates for plane geometry, the definition of Birkhoff & Beatly의 ${\ll}$Basic Geometry${\gg}$. the definition of SMSG ${\ll}$Geometry${\gg}$. and the definition of the similarity concept in current mathematics texts. Then we criticized the definition of the similarity concept in current mathematics texts based on mathematical history. We critically discussed three issues and gave three suggestions.

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.9-18
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• 2006

In this paper we study on concept analogy of altitude and escribed circle of triangle. We start from following theorems related with sides of triangle: existence of triangle, Pythagoras theorem, cosine theorem, Heron formula. Using concept analogy of sides-altitudes, altitudes-escribed circle's radii we discover some properties of altitude and escribed circle's radii and prove these properties.

• Journal of Broadcast Engineering
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• v.24 no.4
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• pp.613-622
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• 2019

A differential codebook design method using wireless channel's temporal correlation is proposed over closed loop multiple-input single-output (MISO) system. The single layer codewords in a codebook are selected among a set of phase elements. In the conventional codeword selection rule, codewords are assumed to be on a spherical cap and sine formula was used. In this paper, however, a new method using Pythagoras formula is employed to simplify computational complexity. Also, an adaptive differential codebook selection is adopted to enhance performance. Monte-Carlo simulations demonstrate that the proposed codebook is superior to the conventional ones.

• Journal of the Korea Society of Computer and Information
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• v.26 no.6
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• pp.37-46
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• 2021

In this paper, we designed and implemented a program to measure and to judge the accuracy of yoga postures using Azure Kinect. The program measures all joint positions of the user through Azure Kinect Camera and sensors. The measured values of joints are used as data to determine accuracy in two ways. The measured joint data are determined by trigonometry and Pythagoras theorem to determine the angle of the joint. In addition, the measured joint value is changed to relative position value. The calculated and obtained values are compared to the joint values and relative position values of the desired posture to determine the accuracy. Azure Kinect Camera organizes the screen so that users can check their posture and gives feedback on the user's posture accuracy to improve their posture.

• Journal for History of Mathematics
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• v.19 no.4
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• pp.63-80
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• 2006

Along with natural and algebraic languages, schema is a fundamental component of mathematical language. The principal purpose of this present study is to focus on this point in detail. Schema was already in use during Pythagoras' lifetime for making geometrical inferences. It was no different in the case of Oriental mathematics, where traces have been found from time to time in ancient Chinese documents. In schma an idea is transformed into something conceptual through the use of perceptive images. It's heuristic value lies in that it facilitates problem solution by appealing directly to intuition. Furthermore, introducing schema is very effective from an educational point of view. However we should keep in mind that proof is not replaceable by it. In this study, various schemata will be presented from a diachronic point of view, We will show with emaples from the theory of categories, Feynman's diagram, and argand's plane, that schema is an indispensable tool for constructing new knowledge.

• The Mathematical Education
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• v.57 no.2
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• pp.93-110
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• 2018

One of the biggest changes in the 2015 revised mathematics curriculum is shifting to the second year of middle school in Pythagorean theorem. In this study, the following subjects were studied. First, Pythagoras theorem analyzed the expected problems caused by the shift to the second year middle school. Secondly, we have researched the reconstruction method to solve these problems. The results of this study are as follows. First, there are many different ways to deal with Pythagorean theorem in many countries around the world. In most countries, it was dealt with in 7th grade, but Japan was dealing with 9th grade, and the United States was dealing with 7th, 8th and 9th grade. Second, we derived meaningful implications for the curriculum of Korea from various cases of various countries. The first implication is that the Pythagorean theorem is a content element that can be learned anywhere in the 7th, 8th, and 9th grade. Second, there is one prerequisite before learning Pythagorean theorem, which is learning about the square root. Third, the square roots must be learned before learning Pythagorean theorem. Optimal positions are to be placed in the eighth grade 'rational and cyclic minority' unit. Third, Pythagorean theorem itself is important, but its use is more important. The achievement criteria for the use of Pythagorean theorem should not be erased. In the 9th grade 'Numbers and Calculations' unit, after learning arithmetic calculations including square roots, we propose to reconstruct the square root and the utilization subfields of Pythagorean theorem.

• Journal for History of Mathematics
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• v.24 no.1
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• pp.15-29
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• 2011

This study was carrying out research on the geometry of Sulbas${\={u}}$tras as parts of looking for historical roots of oriental mathematics, The Sulbas${\={u}}$tras(rope's rules), a collection of Hindu religious documents, was written between Vedic period(BC 1500~600). The geometry of Sulbas${\={u}}$tras in ancient India was studied to construct or design for sacrificial rite and fire altars. The Sulbas${\={u}}$tras contains not only geometrical contents such as simple statement of plane figures, geometrical constructions for combination and transformation of areas, but also algebraic contents such as Pythagoras theorem and Pythagorean triples, irrational number, simultaneous indeterminate equation and so on. This paper examined the key features of the geometry of Sulbas${\={u}}$tras and the geometry of Sulbas${\={u}}$tras for the construction of the sacrificial rite and the fire altars. Also, in this study we compared geometry developments in ancient India with one of the other ancient civilizations.