• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.181-199
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• 2011

The area formula for a plane figure represents the relations between the area and the lengths which determine the area of the figure. Students are supposed to understand the relations in it as well as to be able to find the area of a figure using the formula. This study investigates how 5th grade students understand the formulas for the area of triangle, rectangle and parallelogram, focusing on their understanding of functional relations in the formulas. The results show that students have insufficient understanding of the relations in the area formula, especially in the formula for the area of a triangle. Solving the problems assigned to them, students developed three types of strategies: Substituting numbers in the area formula, drawing and transforming figures, reasoning based on the relations between the variables in the formula. Substituting numbers in the formula and drawing and transforming figures were the preferred strategies of students. Only a few students tried to solve the problems by reasoning based on the relations between the variables in the formula. Only a few students were able to aware of the proportional relations between the area and the base, or the area and the height and no one was aware of the inverse relation between the base and the height.

• Journal of Korean Port Research
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• v.11 no.2
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• pp.257-271
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• 1997

The calculation of earthwork plays a major role in plan or design of many civil engineering projects and thus it has become very important to advanced the accuracy of earthwork calculation. The purpose of this paper is to calculate the excavation volume of terrain using a proposal area formular in eathwork volume determination for reclamation of the harbor. A proposal area formular by first and third equation is compared with end area, middle area, prismoidal formula by trapezoidal, simpson formular to excavation volume for an experimental terrian $1\sim12$. As a result of this study, algorithm of a proposal area formula by prismoidal formula should provide a better accuracy than end area, middle area, prismoidal formula by trapezoidal formular, simpson formular.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.367-373
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• 2006

This study suggests that it is necessary to prove that the values of three areas of a triangle, which are obtained by the multiplication of the respective base and its corresponding height, are the same. It also seeks to deeply understand the meaning of Area formula of triangles by exploring some questions raised in the analysis of the proof. Area formula of triangles expresses the invariance of congruence and additivity on one hand, and the uniqueness of parallel line, one of the characteristics of Euclidean geometry, on the other. This discussion can be applied to introducing and developing exploratory learning on area in that it revisits the ordinary thinking on area.

• The Research Journal of the Costume Culture
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• v.7 no.2
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• pp.275-288
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• 1999

The purpose of this is providing a simple, relatively errorless body surface area calculation. Subjects were 10 married women and 10 singles women whose age was 20 to 29 years old. The Gypsum method has applied for the sampling of body surface. The Weight method has been used to measure body surface by means of transferring gypsum shape on uniform plane polypropylene films. In this study, compare analyzed errors between the traditional formulas for measuring body surface area and measuring data in this experiment. More than all, it has been to induce a regression equation for measuring body surface area, which is so simple to calculate with less errors, with variable factors as weight and height. The results of this experiment as follows : 1. In the traditional formulas, weight formula was shown high average error : Niya\`s height formula. which was modified K value as 0.62 in the height formula (S = KH) is shown lower average error than Lassabliere\`s Height formula. 2. In the weight-height formula (S=K √WH), it was shown high average error according to the increasing of K value. Kawanami\`s formula, which 5.378 as K value, was shown low average error both the singles and the married women. 3. Dubois weight-heingt formula (S=W/sup a/·H/sub b/·K) was shown low average error than the weight, height, weight-height (S=K√WH) formula. 4. The regression equations with variable factors as weight and height are 156.74W + 86.05H - 660.25 (Single women) and 136.02W + 90.57H - 6241.32 (Married women) the average error and absolute average error to the singles are 0.09%, 0.94% and resoectively -0.13%, 1.16% for the married women.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.451-469
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• 2012

This research intends to examine how 6th graders (age 12) conceptualize the area of geometric figures. In this research, 4 problems were given to 122 students, which the 4 problems correspond to understanding area concept, finding the area of geometric figures-including rectangular, parallelogram, and triangle, writing the area formula for finding area of geometric figures, and explaining the reason why the area formula holds. As the results of the study, we identified that students revealed the most low achievement in the understanding area concept, and lower achievement in explaining the reason why the area formula holds, writing the area formula, finding the area of geometric figures in order. In based on the results, we suggested the didactical implication for improving the students' conception about the area of geometric figures.

• Magazine of the Korean Society of Agricultural Engineers
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• v.38 no.2
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• pp.108-122
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• 1996

This study was to introduced estimation model for optimum probabilistic rainfall intensity on hydrological area. Originally, probabilistic rainfall intensity formula have been characterized different coefficient of formula and model following watersheds. But recently in korea rainfall intensity formula does not use unionize applyment standard between administration and district. And mingle use planning formula with not assumption model. Following the number of year hydrological duration adjust areal index. But, with adjusting formula applyment was without systematic conduct. This study perceive the point as following : 1) Use method of excess probability of Iwai to calculate survey rainfall intensity value. 2) And, use method of least squares to calculate areal coefficient for a unit of 157 rain gauge station. And, use areal coefficient was introduced new probabilistic rainfall intensity formula for each rain gauge station. 3) And, use new probabilistic rainfall intensity formula to adjust a unit of fourteen duration-a unit of fifteen year probabilistic rainfall intensity. 4) The above survey value compared with adjustment value. And use three theory of error(absolute mean error, squares mean error, relative error ratio) to choice optimum probabilistic rainfall intensity formula for a unit of 157 rain gauge station.

• Journal of the Korea Safety Management & Science
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• v.22 no.2
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• pp.73-82
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• 2020

IEC 60079-10-1 edition 2.0, the global standard for hazardous area classification, was newly revised in 2015. There are many differences compared to the previous edition 1.0 version, first released in 2008, so it has caused confusion in the industry. In case of edition 1.0, the hazardous area extent can be derived through the mathematical formula, but in case of edition 2.0, there was the problem that the exact hazardous area extent was not known because of the mathematical formula of the plot for applying the hazardous area extent was not presented. In this study, we converted the plot introduced in edition 2.0 to CAD format and derived the plot as the mathematical equations. Through this, we suggest the hazardous area extent formula of three states (heavy gas, diffusive, jet). As the IEC committee did not provide the mathematical formula of the hazardous area extent according to the release characteristic, it is impossible to apply the exact hazardous area extent. In this study, a mathematical approach was derived for the plot introduced in edition 2.0, which can reduce the confusion of the applying hazardous area extent.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.38 no.6
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• pp.991-999
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• 2018

In urban areas, the proportion of railway traffic in public transport is increasing. The congestion situation is repeated as the passengers concentrate on station and transfer facilities and the inconvenience of the passengers is increasing in terms of safety and convenience. Therefore, the importance of estimating the appropriate area of the station has been emphasized. The area estimation formula used in the metropolitan railway stations currently is a partial modification of the area estimation formula of Japan in the 1970s. It does not reflect changes in the social and cultural environment and patterns of passengers. The technical basis for major decision variables is insufficient. Therefore, the theoretical basis of the area estimation formula and the pedestrian environment satisfaction of the design guideline of metropolitan railway stations were analyzed in order to suggest improvement formula. The improved area estimation formula was verified by conducting field surveys on 5 stations of metropolitan railways and 15 stations of urban railways. The existing area estimation formula is LOS E grade for the main space. However, the LOS D grade is implemented when the improved area estimation formula is applied. Based on the results, the design factors for the area estimation formula are suggested.

• Journal for History of Mathematics
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• v.16 no.2
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• pp.43-54
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• 2003

In this article we study various proofs of Heron's formula, extract some didactical ideas from these proofs, and didactically enlarge Heron's formula. In this paper we in detail introduce five different proofs from various articles and textbooks, and suggest our proof of Heron's formula. Enlarging this proof we are able to prove Brahmagupta's formula and generalized convex quadrangle's area formula.

• East Asian mathematical journal
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• v.31 no.2
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• pp.167-188
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• 2015

Formula for the area of a trapezoid is an educational material that can handle algebraic and geometric perspectives simultaneously. In this note, we will make up the expression equivalent algebraically to the formula for the area of a trapezoid, and deal with the conversion of a geometric point of view, in algebraic terms of translating and interpreting the expression geometrically. As a result, the geometric conversion model, the first algebraic model, the second algebraic model are obtained. Therefore, this problem is a good material to understand the advantages and disadvantages of the algebraic and geometric perspectives and to improve the mathematical insight through complementary activity. In addition, these activities can be used as material for enrichment and gifted education, because it helps cultivate a rich perspective on diverse and creative thinking and mathematical concepts.