• The Journal of Korean Association of Computer Education
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• v.4 no.1
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• pp.99-107
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• 2001

One of the main objects of geometry in mathematics education is to improve students' geometric intuition capability and logical reasoning capability based on them. A visual element related to intuition plays an important role in teaching and learning of geometry. Therefore, in this research, we focus on the development of multimedia title available to dynamic operation about visual elements and verify of effect of its application. This title for the learning of "the Pythagorean theorem and its practical use" in the third grade of middle school is designed and implemented by an authoring tool, Toolbook. And it enables learners to study mathematics individually and can be applied to the educational field, too. And we taught two groups, the applied group and the compared one of the second grade of middle school and surveyed Questions and evaluated study achievement. We calculated study achievement of two groups on t-test using SPSS. As the result, we knew that the applied group is higher than the compared one in the study achievement and provision of dynamic operation possibility on visual elements make students know very high learning effect and help improvement of intelligent capability.

• 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.

• Journal of Advanced Marine Engineering and Technology
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• v.37 no.2
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• pp.213-219
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• 2013

Recently, with the rapid advancement in information and communication technology, indoor location-based services(LBSs) that require precise position tracking have been actively studied with outdoor-LBS using GPS. However, in case of a ship which consists of steel structure, it is difficult to measure a precise localization due to significant ranging error by the diffraction and refraction of radio waves. In order to reduce location measurement errors that occur in these indoor environments, this paper presents distance compensation algorithms that are suitable for a narrow passage such as ship corridors without any additional sensors by using UWB(Ultra-wide-band), which is robust to multi-path and has an error in the range of a few centimeters in free space. These improvement methods are that Pythagorean theory and adjacent node technique are used to solve the distance error due to the node deployment and distance variation analysis technique is applied to reduce the ranging errors which are significantly fluctuated in the corner section. The experimental results show that the number of nodes and the distance error are reduced to 66% and 57.41%, respectively, compared with conventional CSS(Chirp spread spectrum) method.

• Journal of the Korean School Mathematics Society
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• v.21 no.4
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• pp.401-418
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• 2018

The current geometric and vector textbooks focus on the mechanical activities of finding focus, corner, etc. through elliptic equations. In this paper, we propose a process in which analogy and analytical methods are used in reversible activities of focusing from a given elliptic graph without a coordinate plane. The exploratory tool was used as Geogebra. At first, students tried to find the focus of the ellipse by randomly constructing the major a is and the minor a is in the given ellipse. However, we have experienced a method of constructing the circle of symmetry and analyzed this principle and deduced it to the ellipse. As a result, we could construct the center, long a is and short a is of the ellipse. Then, using the analytical method, the focus formula was recognized as the Pythagorean theorem, and the ellipse's focus was constructed by using the original drawing. Therefore, it is confirmed that analogy and analytical method can positively affect the elliptical focus.

• The Journal of the Acoustical Society of Korea
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• v.38 no.3
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• pp.302-307
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• 2019

In modern Anti-Submarine Warfare, there are various ways to locate a submarine in a two-dimensional space. For more effective tracking and attack against a submarine the depth of the target is a critical factor. However, it has been difficult to find out the depth of a submarine until now. In this paper a possible solution to the depth estimation of submarines is proposed utilizing DIFAR (Directional Frequency Analysis and Recording) sonobuoy information such as contact bearings at or prior to CPA (Closest Point of Approach) and the target's Doppler signals. The relative depth of the target is determined by applying the Pythagorean theorem to the slant range and horizontal range between the target and the hydrophone of a DIFAR sonobuoy. The slant range is calculated using the Doppler shift and the target's velocity. the horizontal range can be obtained by applying a simple trigonometric function for two consecutive contact bearings and the travel distance of the target. The simulation results show that the algorithm is subject to an elevation angle, which is determined by the relative depth and horizontal distance between the sonobuoy and target, and that a precise measurement of the Doppler shift is crucial.

• Restorative Dentistry and Endodontics
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• v.47 no.1
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• pp.1.1-1.13
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• 2022

Objectives: This study assessed the shape and anatomical relationship of the mental foramen (MF) to mandibular posterior teeth in an Indian sub-population. Materials and Methods: In total, 475 existing cone-beam computed tomography records exhibiting 950 MFs and including the bilateral presence of mandibular premolars and first molars were assessed. Images were evaluated 3-dimensionally to ascertain the position, shape, and anatomical proximity of MFs to mandibular teeth. The position and shape of MFs were measured and calculated. The Pythagorean theorem was used to calculate the distance between the root apex of the mandibular teeth and the MF. Results: MFs exhibited a predominantly round shape (left: 67% and right: 65%) followed by oval (left: 30% and right: 31%) in both males and females and in different age groups. The root apices of mandibular second premolars (left: 71% and right: 62%) were closest to the MF, followed by distal to the first premolars and mesial to the second premolars. The mean vertical distance between the MF and the nearest tooth apex calculated on sagittal sections was 2.20 mm on the right side and 2.32 mm on the left side; no significant difference was found according to sex or age. The distance between the apices of the teeth and the MF was ≥ 4 mm (left; 4.09 ± 1.27 mm and right; 4.01 ± 1.15 mm). Conclusions: These findings highlight the need for clinicians to be aware of the location of the MF in treatment planning and while performing non-surgical and surgical endodontic procedures.

• The korean journal of orthodontics
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• v.37 no.5
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• pp.319-330
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• 2007

Defining right and left side differences in mandibular ramus height is one of the key elements in the diagnosis of facial asymmetry. The purpose of the present study was to evaluate the effect of correction of ramus height with frontal and lateral ramal inclinations (FRI and LRI) in 2-dimensional cephalograms and observe how this affects the diagnostic accuracy of asymmetry. Methods: Frontal and lateral cephalograms were obtained in 40 individuals with chin deviation. FRI and LRI were measured on each side and ramus height measurement was corrected with these inclinations using Pythagorean's theorem. The results of diagnosis before and after correction on cephalograms were compared with the results in 3D CT images. Results: Both FRI and LRI showed greater values in the contralateral side than in the chin-deviated side and these contributed to an increase in the right and left side ramus height differences. After comparison of diagnostic results before and after correction on cephalograms with the results on 3D CT images, the sensitivity increased significantly (from 74 to 94 %) whereas the specificity decreased (from 44 to 22 %). Overall accuracy increased from 68 to 78 % with the correction using FRI and LRI. Conclusions: The results of the present study indicate that correction of ramus height with FRI and LRI is useful for an accurate diagnosis of facial asymmetry on frontal cephalograms.