• Journal for History of Mathematics
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• v.13 no.2
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• pp.121-132
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• 2000

In this paper, we demonstrate the Pythagorean Theorem by using the computer geometric software, Geometer's Skechpad(GSP) in stead of Eucliean logical proof. Also, we show that two applications of Pythagorean Theorem. The one is constructed by the fact that $ka^2+kb^2=kc^2$, where k is a constant, the other is made by the fractal.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.511-528
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• 2010

Students' intuition in formal proof should be expressed as symbols according to the deductive process. The symbol will play a role of the mediation between the intuition and the formal proof. This study examined the evolution process of intuition mediated by the symbol in geometry proof. According to the results first, symbol took the great roles when students had the non-formed intuition for the proposition. The signification of symbols could explain even the proof process of the proposition with the non-expectable intuition. And when students proved it by symbols, not by figure nor words, they could evolute the conclusive intuition about the proposition.

• 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.

• Journal of Advanced Navigation Technology
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• v.19 no.6
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• pp.558-563
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• 2015

There have recently been various services that use indoor location estimation technologies. Representative methods of location estimation include fingerprinting and triangulation, but they lack accuracy. Various kinds of research which apply existing location estimation methods like AOA, TOA, and TDOA are being done to solve this problem. In this paper, we study the location estimation algorithm based on AOA using a RSSI difference in indoor environments. We assume that there is a single AP with four antennas, and estimate the angle of arrival based on the RSSI value to apply the AOA algorithm. To compensate for RSSI, we use a recursive averaging filter, and use the corrected RSSI and the Pythagorean theorem to estimate the angle of arrival. The results of the experiment, show an error of 18% because of the radiation pattern of the four non-directional antennas arranged at narrow intervals.

• 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.

• 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.