• East Asian mathematical journal
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• v.37 no.4
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• pp.401-426
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• 2021

In order to propose ways to implement mathematical connection between algebra and geometry, this study reinterpreted and visualized the Khayyam's geometric method solving the cubic equations using two conic sections and the Al-Kāshi's method of constructing of angle trisection using a cubic equation. Khayyam's method is an example of a geometric solution to an algebraic problem, while Al-Kāshi's method is an example of an algebraic a solution to a geometric problem. The construction and property of conics were presented deductively by the theorem of "Stoicheia" and the Apollonius' symptoms contained in "Conics". In addition, I consider connections that emerged in the alternating process of algebra and geometry and present meaningful Implications for instruction method on mathematical connection.

• Geomechanics and Engineering
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• v.35 no.2
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• pp.181-194
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• 2023

The primary objective of this study is to examine the influence of geometry on the stability characteristics of cylindrical microstructures. This investigation entails a stability analysis of a bi-directional functionally graded (BD-FG) cylindrical imperfect concrete beam, focusing on the impact of geometry. Both the first-order shear deformation beam theory and the modified coupled stress theory are employed to explore the buckling and dynamic behaviors of the structure. The cylinder-shaped imperfect beam is constructed using a porosity-dependent functionally graded (FG) concrete material, wherein diverse porosity voids and material distributions are incorporated along the radial axis of the beam. The radius functions are considered in both uniform and nonuniform variations, reflecting their alterations along the length of the beam. The combination of these characteristics leads to the creation of BD-FG configurations. In order to enable the assessment of stability using energy principles, a numerical technique is utilized to formulate the equations for partial derivatives (PDEs).

• Journal of Mechanical Science and Technology
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• v.17 no.9
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• pp.1349-1357
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• 2003

This paper deals with verification of the theoretical model for dynamic behavior of Pipeline Inspection Gauge (PIG) traveling through high pressure natural gas pipeline. The dynamic behavior of the PIG depends on the differential pressure across its body. This differential pressure is generated by injected gas flow behind the tail of the PIG and expelled gas flow in front of its nose. To analyze the dynamic behavior characteristics such as gas flow in pipeline, and the PIG position and velocity, not only the mathematical models are derived, but also the theoretical models must be certified by actual pigging experiment. But there is not any found results of research on the experimental certification for dynamic behavior of the PIG. The reason is why the fabrication of the PIG as well as, a field application are very difficult. In this research, the effectiveness of the introduced solution using the method of characteristics (MOC) was certified through field application. In-line inspection tool, 30" geometry PIG, was fabricated and actual pigging was carried out at the pipeline segment in Korea Gas Corporation (KOGAS) high pressure system, Incheon LT (LNG Terminal) -Namdong GS (Governor Station) line. Pigging is fulfilled successfully. Comparison of simulation results with experimental results show that the derived mathematical models and the proposed computational schemes are effective for predicting the position and velocity of the PIG with a given operational conditions of pipeline.

• The Mathematical Education
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• v.60 no.4
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• pp.543-554
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• 2021

The dynamic geometric environment plays a positive role in solving students' geometric problems. Students can infer invariance in change through dragging, and help solve geometric problems through the analysis method. In this study, the continuous spectrum of the dynamic geometric environment can be used to solve problems of students. The continuous spectrum can be used in the 'Understand the problem' of Polya(1957)'s problem solving stage. Visually representation using continuous spectrum allows students to immediately understand the problem. The continuous spectrum can be used in the 'Devise a plan' stage. Students can define a function and explore changes visually in function values in a continuous range through continuous spectrum. Students can guess the solution of the optimization problem based on the results of their visual exploration, guess common properties through exploration activities on solutions optimized in dynamic geometries, and establish problem solving strategies based on this hypothesis. The continuous spectrum can be used in the 'Review/Extend' stage. Students can check whether their solution is equal to the solution in question through a continuous spectrum. Through this, students can look back on their thinking process. In addition, the continuous spectrum can help students guess and justify the generalized nature of a given problem. Continuous spectrum are likely to help students problem solving, so it is necessary to apply and analysis of educational effects using continuous spectrum in students' geometric learning.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.8
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• pp.349-356
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• 2001

The dynamic behavior of high speed train is very Important because the railway should be safe and Is satisfied tilth the rode comfort of passengers. The train is composed of many suspension components. such as 1st springs, 1st dampers, 2nd springs and 2nd dampers, that have an influence on the dynamic characteristics of high speed train. Also, the wheel/rail shapes, the track conditions and geometry and many environmental factors, such as rain, snow and wind. affect the dynamic behavior of high speed train. This paper reviews the effect of wind and track conditions on the dynamic behavior of high speed train. The VAMPIRE program Is used for this simulation. The result of simulation shows that the high speed train should not be operated when the wind velocity is beyond 34.5 m/sec.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.4
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• pp.38-45
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• 1997

A new dynamic model for the cutting process inb the end milling process is developed. This model, which describes the dynamic response of the end mill, the chip load geometry including tool runout, the dependence of the cutting forces on the chip load, is used to predict the dynamic cutting force during the end milling process. In order to predict accurately cutting forces and tool vibration, the model which uses instantaneous specific cutting force, inclueds both regenerative effect and penetration effect, The model is verified through comparisons of model predicted cutting force with measured cutting force obtained from machining experiments.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.3 s.180
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• pp.39-46
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• 2006

In this work a dynamic cutting force model in ball end milling of inclined surface is introduced. To represent the complex cutting geometry in ball end milling of inclined surface, workpiece is modeled with Z-map method and cutting edges are divided into finite cutting edge elements. As tool rotates and vibrates, a finite cutting edge element makes two triangular sub-patches. Using the number of nodes in workpiece which are in the interior of sub-patches, instant average uncut chip thickness is derived. Instant dynamic cutting forces are computed with the chip thickness and cutting coefficients. The deformation of cutting tool induced by cutting farces is also computed. With iterative computation of these procedures, a dynamic cutting force model is generated. The model is verified with several experiments.

• Journal of the Korean Society for Railway
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• v.4 no.4
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• pp.131-137
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• 2001

The dynamic behavior of high speed train is very important because of its safety and passengers' ride comfort. The railway vehicle is composed of many suspension components, such as 1st springs, 1st dampers, 2nd springs and 2nd dampers, that have an influence on the dynamic characteristics of high speed train. Also, the wheel/rail shapes and the track geometry affect the dynamic behavior of high speed train. This paper reviews the dynamic behavior of KHST in the KTX test line. The VAMPIRE program is used for this simulation. The simulation results are within the limits of safety criteria. Thus the KHST can operate safely at 350 km/h in the KTX test line.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.495-500
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• 2001

The dynamic behavior of high speed train is very important because it should be safe and is satisfied with the ride comfort of passengers. The railway is composed of many suspension components-1st springs, 1st dampers, 2nd springs, 2nd dampers etc- that have an influence on the dynamic characteristics of high speed train. Also, the wheel/rail shapes, the track condition and geometry and many environmental factors-rain, snow, wind etc-are affected the dynamic behavior of high speed train. This paper is reviewed the effect of wind(gust) on the dynamic behavior of high speed train. Vampire program is used for this simulation. The result of simulation shows that high speed train should not be operated when the gust speed is beyond 34.5m/sec.

• Proceedings of the KSR Conference
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• 2011.10a
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• pp.337-342
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• 2011

Vehicle dynamic behavior should be investigated to establish the track irregularity criteria because they have an impact on vehicle dynamic behavior. The influence of twist on running behavior and safety for KTX was instigated by numerical analysis among track geometry quality parameters such as vertical alignment, lateral alignment, twist and track gauge in this paper. The wavelength and amplitude of twist were considered in scenario of this numerical analysis. This research is based on just numerical analysis and the final result which include measurement will be published in the future.