• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.499-524
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• 2015

In the present study, we propose four participating $8^{th}$ grade students' genetic decomposition of congruent transformation and investigate the role of their dragging activities while understanding the concept of congruent transformation in GSP(Geometer's Sketchpad). The students began to use two major schema, 'single-point movement' and 'identification of transformation' simultaneously in their transformation activities, but they were inclined to rely on the single-point movement schema when dealing with relatively difficult tasks. Through dragging activities, they could expand the domain and range of transformation to every point on a plane, not confined to relevant geometric figures. Dragging activities also helped the students recognize the role of a vector, a center of rotation, and an axis of symmetry.

• 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 the Korean Society for Precision Engineering
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• v.11 no.4
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• pp.77-87
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• 1994

This paper deals with an automated forming sequence design system by which designers can determine desirable operation sequences even if they have little experience in the design of cold forging process. The forming sequence design in the cold forging is very important and requires many kinds of technical and empirical knowledge. They system isproposed, which generates forming sequence plans for the multistage cold forging of axisymmtrical solid products. Since the process of metal forming can be considered as a transformation of geometry, treatment of the geometry of the product is a key in planning process. To recognize the geometry of the product section, section entity representation and primitive geometries were used. Section entity representation can be used for the calculation of maximum diameter, maximum height, and volume. Forming sequence for the part can be determined by means of primitive geometries such as cylinder, cone, convex, and concave. By utilizing this geometrical characteristics (diameter, height, and radius), the product geometry is expressed by a list of the priitive geometries. Accordingly the forming sequence design is formulated as the search problem which starts with a billet geometry and finishes with a given product one. Using the developed system, the sequence drawing with all dimensions, which includes the proper sequence of operations for the part, is generated under the environment of AutoCAD. Based on the results of forming sequence, process variables(strain, punch pressure, die inner pressure, and forming load) are determined.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1121-1125
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• 2003

In this paper we deal with visual servoing that can control a robot arm with a camera using information of images only, without estimating 3D position and rotation of the robot arm. Here it is assumed that the robot arm is calibrated and the camera is uncalibrated. We use a pinhole camera model as the camera one. The essential notion can be show, that is, epipolar geometry, epipole, epipolar equation, and epipolar constrain. These play an important role in designing visual servoing. For easy understanding of the proposed method we first show a design in case of the calibrated camera. The design is constructed by 4 steps and the directional motion of the robot arm is fixed only to a constant direction. This means that an estimated epipole denotes the direction, to which the robot arm translates in 3D space, on the image plane.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2001.10a
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• pp.75-80
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• 2001

The purpose of this study is to investigate the characteristics of springback for various process conditions of the 2D draw-bending operation. The process variables are the forming temperature, the geometry of tools such as punch profile radius(Rp) and die profile radius(Rd). Especially, in order to control the springback, the use of the warm forming method is applied. For the warm draw-bending, five steps of temperature ranges, from room temperature to $200^{\circ}C$, were adopted. And two kinds of steel sheets, namely SCP1 and TRIP(transformation-induced plasticity), the newly developed high strength Steel, were adopted. As a result, the springback was affected by the elevated temperature and the geometry of tools in two kinds of steel sheets.

• Proceedings of the KOSOMBE Conference
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• v.1994 no.05
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• pp.131-135
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• 1994

In order to study the shape and dimensions of heart, the procedures to reconstruct a three dimensional left ventricular geometry from two dimensional echocardiographic images is studied including the coordinate transformation, curve fitting and interpolation utilizing three dimensional position registration arm. Nonlinear material property of the left ventricular myocardium was obtained by finite element method performed on the reconstructed geometry and optimization techniques which compare the computer predicted 3D deformation with the experimentally determined deformation. Afterwards using the obtained nonlinear material propertry the stress distribution related with oxyzen consumption rate was analyzed.

• The Journal of Korea Robotics Society
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• v.8 no.3
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• pp.179-185
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• 2013

In this paper we propose a haptic interaction system that physically represents the underlying geometry of objects displayed in a 2D picture, i.e., a digital image. To obtain the object's geometry displayed in the picture, we estimate the physical transformation between the object plane and the image plane based on homographic information. We then calculate the rotated surface normal vector of the object's face and place it on the corresponding part in the 2D image. The purpose of this setup is to create a force that can be rendered along with the image without distorting the visual information. We evaluated the proposed haptic rendering system using a set of pictures of objects with different orientations. The experimental results show that the participants reliably identified the geometric configuration by touching the object in the picture. We conclude this paper with a set of applications.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.03b
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• pp.269-272
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• 1999

It is still hard to measure the strain distribution over entire surface of a medium or large-size stamped part even by using an automated strain measurement system. Several methods which enable to enlarge the measurement range without losing accuracy and precision are suggested in this study, The superposition of images having different high-lightened or damaged part each other results in an enhanced image. A new method for constructing the element connectivity from a line-thinned image makes it possible to identify up to 1,000 elements. And the geometry assembling algorithm is proved very efficient in which the whole area to be measured is divided into several parts ; the coordinate transformation between every two adjacent parts is obtained from the concept of the least square error ; and the 3-D shape or strain distribution over the whole surface is assembled,

• Journal of the Korean Society for Precision Engineering
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• v.12 no.5
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• pp.46-56
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• 1995

As demands on the precision bevel gears are increased in the related industry, the exact kinematical investigations of a pair of spherical involute bevel gears are required for the computer aided design. The exact angular velocity ratio based on the characteristics of the spherical involute tooth is derived and verified from the relationship between rotational angles. Elementary kinematics of the gearsets is investigated by applying the transformation of the coordinate systems. The tooth contact lines based on logarithmic tooth-wise curve are examines in three dimentional space. Contact ratio is formulated and simulated according to the system parameters such as shaft angles, pressure angle, and spiral angles. The condition of teeth interference is dervied and the critical numbers of gear teeth are calculated. The whole surface geometry of a spiral bevel gearsets are discretized and visualized by a computer graphic tool.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.77-86
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• 2004

Felix Klein profoundly influenced mathematical developments throughout the world by showing a new direction for modem geometry. He also influenced the lives of excellent scientists like Einstein by reforming mathematical education. The first Felix Klein medal of the Internal Commission on Mathematical Instruction was awarded at ICME-10 in July of 2004. In this article, we discuss Klein's Erlangen Program and investigate his influence on modem mathematics and mathematical education with this medal as momentum.