• 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.

• School Mathematics
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• v.8 no.3
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• pp.327-339
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• 2006

In this study, a teaching units for teaching and learning of secondary preservice teachers' mathematising is designed, focusing on reinvention of Bretschneider's formula. preservice teachers can obtain the following through this teaching units. First, preservice teachers can experience mathematising which invent a noumenon which organize a phenomenon, They can make an experience to invent Bretscheider's formula as if they invent mathematics really. Second, preservice teachers can understand one of the mechanisms of mathematics knowledge invention. As they reinvent Brahmagupta's formula and Bretschneider's formula, they understand a mechanism that new knowledge is invented Iron already known knowledge by analogy. Third, preservice teachers can understand connection between school mathematics and academic mathematics. They can understand how the school mathematics can connect academic mathematics, through the relation between the school mathematics like formulas for calculating areas of rectangle, square, rhombus, parallelogram, trapezoid and Heron's formula, and academic mathematics like Brahmagupta's formula and Bretschneider's formula.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.4C
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• pp.254-264
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• 2011

In this paper, we propose two algorithm for improving the performance of wireless localization(Trilateration and Least Square) based on the range based approach method in indoor environment using RSSI for ranging distance. we propose a method to discriminate the case that has relatively large estimation errors in trilateration using Heron''s formula for the volume of a tetrahedron. And we propose the algorithm to process the discriminated types of distance using the absolute value calculated by Heron''s formula. In addition, we propose another algorithm for the case of which the number of anchor nodes larger than three. In this case, Residual Weighting Factor(RWGH) improves the performance of Least Square. However, RWGH requires many number of calculations. In this paper, we propose Iterative Weighted Centroid Algorithm(IWCA) that has better performance and less calculation than RWGH. We show the improvement of performance for two algorithms and the combination of these algorithm by using simulation results.

• International Journal of Advanced Culture Technology
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• v.6 no.3
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• pp.216-225
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• 2018

Strangely enough, there has not been much effort in applying the latest technologies to help referees make accurate calls in a soccer game compared to other sports. Modern soccer tries to apply VAR (Video Assistant Referee) technology to correct inaccurate calls such as an offside, but this is being put off due to the fact that real time decision-making cannot be carried out by using this technology. This has led this study to decide developing a device that will accurately identify offsides on a real time basis using various latest sensors and related technologies. This device will aid referees in calling offsides in a soccer match.

• Journal of Korean Foot and Ankle Society
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• v.11 no.2
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• pp.123-129
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• 2007

Purpose: The aim of this study was to analyze radiological change of Kager's triangle in patients with retrocalcaneal disorders. Materials and Methods: Areas of Kager's triangle and calcaneus were calculated with Heron's Formula. Average of area ratio (area of Kager's triangle / area of calcaneus) was calculated for comparison and analysis, according to disease activity and aging process. One-tailed Z-test was done with the average of area ratio. Results: Average of area ratio (area of Kager's trianlge / area of calcaneous) tends to decrease according to aging process and disease existence. Conclusion: Because area of Kager's triangle in patients with retrocalcaneal disorders tends to change according to disease activity and aging process, we should consider clinical correlation between the anatomical structure of Kager's triangle and retrocalcaneal symptoms.

• 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.

• KIPS Transactions on Computer and Communication Systems
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• v.3 no.7
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• pp.241-244
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• 2014

Wireless Sensor Network(WSN) has been attracting lots of interest in recent years for smart surveillance systems. WSN-based surveillance systems need to figure out the occurrence or existence of events or objects and to find out where the events have occurred or the objects are present. In our surveillance system, it is needed to give an alarm only when the detected object is human (not pets or rodents) for reducing false alarms and improving the system reliability. In this paper, we propose a height prediction mechanism to determine if the detected object is human using Heron's formula. Finally, we verify the performance of our proposed mechanism through various experiments.