• Research in Mathematical Education
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• v.18 no.1
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• pp.1-29
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• 2014

When taught the precise definition of ${\pi}$, students may be simply asked to memorize its approximate value without developing a rigorous understanding of the underlying reason of why it is a constant. Measuring the circumferences and diameters of various circles and calculating their ratios might just represent an attempt to verify that ${\pi}$ has an approximate value of 3.14, and will not necessarily result in an adequate understanding about the constant nor formally proves that it is a constant. In this study, we aim to investigate prospective teachers' conceptual understanding of ${\pi}$, and as a constant and whether they can provide a proof of its constant property. The findings show that prospective teachers lack a holistic understanding of the constant nature of ${\pi}$, and reveal how they teach students about this property in an inappropriate approach through a proving activity. We conclude our findings with a suggestion on how to improve the situation.

• Communications of Mathematical Education
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• v.20 no.3 s.27
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• pp.373-389
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• 2006

The purpose of this study is to compare the way of proving using combinational proof with the way of proving presented in the existing math textbook in the proof of combinational equation and to classify the problem-solving into some categories using combinational proof in combinational equation. Corresponding with these, this study suggests the application of combinational equation using combinational proof and the fundamental material to develop material for advanced study.

• Korean Journal of Geomatics
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• v.2 no.2
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• pp.91-98
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• 2002

Lands along the coast may be submerged in high water because of erosion by sea water, collapsing by itself, excavation by animals, and by tidal movement. From a cadastral point of view, some mistakes in registering a parcel located along the coast may cause the parcel to seem to be collapsed. Therefore, geological, physical oceanographic, and cadastral and topographic investigation are necessary to verify that the submerged land in high water collapsed after it was registered. This paper presents a cadastral and topographic investigation for proving a parcel has collapsed under the sea after registered. In this study, cadastral records and the boundary on cadastral maps were examined carefully to find any errors in them. If the topographic maps were drawn when the parcel was registered, it is good proof of topography of the land at that time. Topographic maps drawn recently were compared to those in the 1900s and in 1970s. In conclusion, cadastral records and maps as well as topographic maps play an important role in proving whether lands along the coast were collapsed or not.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.8 s.113
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• pp.806-813
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• 2006

An important factor of vibration test using MAST(multi axial simulation table) system is the reliance of input excitation source. Generally the generation of input excitation source is obtained by the measured data on special road in proving ground. The measured data on special road have more exciting energy than the data of real fields, therefore the time and expense for test can be reduced. But the magnitude of input excitation source must be defined by comparison with the excited energy on real field. The object of this paper makes the data base of domestic roads for the definition of input excitation source which is obtained by the measured data on special road in proving ground. These real field data on domestic roads are analyzed by the power spectral density and interrelationship index.

• The Korean Nurse
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• v.21 no.2 s.115
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• pp.71-81
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• 1982

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.47-51
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• 1994

The purpose of this note is to give a new selection theorem which is an essential tool for proving the new kind of existence theorem of the equilibrium price comparable to the Debreu-Gale-Nikaido theorem.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.1
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• pp.259-266
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• 1990

Leaks at the piston seal and the by-pass port of a small volume prover have relatively large influence on the proving accuracy in comparison with a conventional ball prover. The pulse interpolator, which is to increase the discrimination, is affected by the characteristic of the flowmeter signal. In this study, a small volume prover of the double cylinder type was designed in order to study the pulse interpolation error as well as the leak error. The basic volume of the prover determined by a water draw method was about 9.68L. Experimental results revealed that interpolation data attained by the repeated piston pass for turbine meters at a fixed flowrate may be treated effectively by applying a statistical method. It was possible to limit the pulse interpolation error less than .+-. 0.02% at the 95% confidence level. However, in the case of the bulk meter, if failed to achieve the required repeatability level because of the pulse characteristics. The basic volume change appeared to be independent of the piston velocity within the .+-. 0.05% of tolerance.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.297-302
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• 2007

Vibrating test of vehicle component can be possible in lab-based simulators instead of field testing owing to the development of technology in control algorithm as well as computational process. Currently, Multi-Axial Simulation Table(MAST) is recommended as a vibrating equipment, which excites a target component for 3-directional translation and rotation motion simultaneously and hence, vibrational condition can be fully approximated to that of real road test. But, the vibration-free performance of target component is not guaranteed with MAST system, which is only simulator subjective to the operator. Rather, the reliability of multi-axial vibration test is dependent on the quality of input profile which should cover the required severity of vibrating condition on target component. In this paper, multi-axial vibration testing methodology of vehicle component is presented here, from data acquisition of vehicle accelerations to the obtaining the input profile of MAST using severe data at proving ground. To compare the severity of vibration condition, between real road test and proving ground one, energy principle of equivalent damage is proposed to calculate energy matrices of acceleration data and then, it is determined the optimal combination of special events on proving ground which is equivalent to real road test at the aspects of vibration fatigue using sequential searching optimal algorithm. To explain the vibration methodology clearly, seat and door component of vehicle are selected as a example.

• The Transactions of the Korea Information Processing Society
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• v.4 no.5
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• pp.1243-1256
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• 1997

Object modeling has been cinsidered as an efficient technique for eleciting user requirements and communicat-ing between developers and customers. But model itself is not easy to understand what recult will be after coding and whether it will be meet with the requirements of customers. In this paper, we developed the envuroment for visualization of object model for validating with rewuirnent at the early stage. Therefore, we defined correct and complete rules which can transform the object model.the delierables of Shler/Mellor's method, into a for-mal specification language of VDM(Vienna Development Methods) with a mathematical basis. This basis provides the means of proving that a specification is realizable and proving properties of a system.Therefore.the completeness, preciceness of object model can be verified by proving the transformed VDM specification and prototyping by constructing a visualization supporting enviroment.

• The Mathematical Education
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• v.63 no.2
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• pp.139-163
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• 2024

The purpose of this study is to examine the capabilities of ChatGPT as a tool for supporting students in generating mathematical arguments that can be considered proofs. To examine this, we engaged students enrolled in a mathematics pathways course in evaluating and revising their original arguments using ChatGPT feedback. Students attempted to find and prove a method for the area of a triangle given its side lengths. Instead of directly asking students to prove a formula, we asked them to explore a method to find the area of a triangle given the lengths of its sides and justify why their methods work. Students completed these ChatGPT-embedded proving activities as class homework. To investigate the capabilities of ChatGPT as a proof tutor, we used these student homework responses as data for this study. We analyzed and compared original and revised arguments students constructed with and without ChatGPT assistance. We also analyzed student-written responses about their perspectives on mathematical proof and proving and their thoughts on using ChatGPT as a proof assistant. Our analysis shows that our participants' approaches to constructing, evaluating, and revising their arguments aligned with their perspectives on proof and proving. They saw ChatGPT's evaluations of their arguments as similar to how they usually evaluate arguments of themselves and others. Mostly, they agreed with ChatGPT's suggestions to make their original arguments more proof-like. They, therefore, revised their original arguments following ChatGPT's suggestions, focusing on improving clarity, providing additional justifications, and showing the generality of their arguments. Further investigation is needed to explore how ChatGPT can be effectively used as a tool in teaching and learning mathematical proof and proof-writing.