• Communications of the Korean Mathematical Society
• /
• v.12 no.4
• /
• pp.985-998
• /
• 1997

For n random strips chosen so as to meet a fixed bounded convex set K of the plane we let $\nu$ be the number of intersection regions that meet K. We develop the integral formula for the mean value of $\nu$ and $\nu^2$ involving the area and the perimeter of K and the breadths of the strips. We get some geometric inequalities in way of studying integral geometry.

• Journal of the Korean School Mathematics Society
• /
• v.15 no.1
• /
• pp.183-197
• /
• 2012

Geometry having long history of mathematics have important role for thinking power and creativity progress in middle school. The regular polygon included in plane geometry was mainly taught convex regular polygon in elementary school and middle school. In this study, we investigated the denotation's extension of regular polygon by mathematical basic knowledge included in school curriculum. For this research, first, school mathematical knowledge about regular polygon was analyzed. And then, basic direction of research was established for inquiry. Second, based on this analysis inductive inquiry activity was performed with research using geometry software(Cabri Geometry II). Through this study the development of enriched learning material and showing the direction of geometry research is expected.

• Korean Journal of Computational Design and Engineering
• /
• v.4 no.2
• /
• pp.162-171
• /
• 1999

Plane sweep plays an important role in computational geometry. This paper shows that an extension of topological plane sweep to three-dimensional space can calculate the volume swept by rotating a solid polyhedral object about a fixed axis. Analyzing the characteristics of rotational swept volumes, we present an incremental algorithm based on the three-dimensional topological sweep technique. Our solution shows the time bound of O(n²·2?+T?), where n is the number of vertices in the original object and T? is time for handling face cycles. Here, α(n) is the inverse of Ackermann's function.

• Journal for History of Mathematics
• /
• v.31 no.6
• /
• pp.315-337
• /
• 2018

Pythagorean thoerem exists in several equivalent forms in the Euclidean plane, that is, the Hilbert plane which in addition satisfies the parallel axiom. In this article, we investigate the truthness and mutual relationships of those propositions in various non-Hilbert planes which satisfy the parallel axiom and all the Hilbert axioms except the SAS axiom.

• Proceedings of the Korean Vacuum Society Conference
• /
• 1999.07a
• /
• pp.169-169
• /
• 1999

We studied magnetic properties of co thin films deposited on Pd (111) surface, which attracted much attention recently due to the perpendicular magnetic anisotropy, using magnetic circular dichroism(MCD). Special attention was paid on the effect of Pd capping and interface roughness on the direction of magnetic easy axis, and for that purpose MCD signals for all Co thicknesses were measured with two different ways : in-plane and out-of-plane geometry. In case of bare Co films deposited on smooth Pd(111) surface, no MCD signal was observed under 4$\AA$ co thickness. At 4$\AA$ Co thickness, MCD signal at the out-of-plane geometry was observed, and for thicker Co films, only in-plane MCD signal was measured. This type of magnetic easy axis transition has been reported for other cases like Co/Pt system. The effect of 5$\AA$ Pd capping on these bare Co films made an remarkable change on the transition of magnetic easy axis. Out-of-plane MCD signals exists up to 20$\AA$ Co thickness, and disappears at 24$\AA$ Co thickness. In-plane MCD signals first appears at 10$\AA$ Co thickness and gradually increases up to 24$\AA$ Co thickness. Between 10$\AA$ and 20$\AA$ Co thickness, in-plane and out-of-plane MCD signal coexist. The formation of multi-domain structure or the existence of tilted magnetic easy axis is an possible scenario for such an interesting coexistence. The effect of interface roughness was also tested by measuring MCD signal on Co films deposited on un-annealed Pd(111) surface. Out-of-plane MCD signal was observed up to 8$\AA$ Co thickness and the anisotropy of MCD signal at 4$\AA$ Co thickness was very large with respect to that of Co film deposited on the smooth substrate. Above 8$\AA$ thickness, there exists only in-plane MCD signal. From above results, it was concluded that both Pd capping and interface roughness induce and reenforce the perpendicular magnetic anisotropy. The large perpendicular magnetic anisotropy of Co/Pd multilayer system made by sputtering method can be well understood from our results.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.10
• /
• pp.2172-2179
• /
• 2002

In this paper, we examine the dynamic electromechanical behavior of an edge crack in a piezoelectric ceramic layer bonded between two elastic layers under the combined anti-plane mechanical shear and in-plane electric transient loadings. We adopted both the permeable and impermeable crack boundary conditions. Fourier transforms are used to reduce the problem to the solution of two pairs of dual integral equations, which are then expressed to a Fredholm integral equation of the second kind. Numerical values on the dynamic energy release rate are presented to show the dependences upon the geometry, material combination, electromechanical coupling coefficient and electric field.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.20 no.3
• /
• pp.339-345
• /
• 2007

In this paper, a variational formulation for plane elasticity problems is derived based on an isogeometric approach. The isogeometric analysis is an emerging methodology such that the basis functions for response analysis are generated directly from NURBS (Non-Uniform Rational B-Splines) geometry. Furthermore, the solution space for the response analysis can be represented in terms of the same functions to represent the geometry, which enables to provide a precise construction method of finite element model to exactly represent geometry using B-spline base functions in CAD geometric modeling and analyze arbitrarily shaped structures without re-meshing. In this paper, a continuum-based adjoint sensitivity analysis method using the isogeometric approach is extensively derived for the plane elasticity problems. The conventional shape optimization using the finite element method has some difficulties in the parameterization of geometry In the isogeometric analysis, however, the geometric properties are already embedded in the B-spline basis functions and control points so that it has potential capability to overcome the aforementioned difficulties. Through some numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.

• Journal of Educational Research in Mathematics
• /
• v.16 no.1
• /
• pp.1-23
• /
• 2006

It is regarded as critical to analyse and re-appreciate Euclidean geometry for the sake of improving school geometry This study, a critical analysis of demonstrative plane geometry in current secondary school mathematics with an eye to the viewpoints of 'Elements of Geometry', is conducted with this purpose in mind. Firstly, the 'Elements' is analysed in terms of its educational purpose, concrete contents and approaching method, with a review of the history of its teaching. Secondly, the 'Elemens de Geometrie' by Clairaut and the 'histo-genetic approach' in teaching geometry, mainly the one proposed by Branford, are analysed. Thirdly, the basic assumption, contents and structure of the current textbooks taught in secondary schools are analysed according to the hypothetical construction, ordering and grouping of theorems, presentations of proofs, statements of definitions and exercises. The change of the development of contents over time is also reviewed, with a focus on the proportional relations of geometric figures. Lastly, tile complementary way of integrating the two 'Elements' is explored.

• Geomechanics and Engineering
• /
• v.12 no.6
• /
• pp.983-1001
• /
• 2017

The extent by which economy and safety concerns can be addressed in earth retaining structure design depends on the accuracy of the assumed failure surface. Accordingly, this study attempts to investigate and quantify mechanical backfill properties that control failure surface geometry of cohesionless backfills at the active state for translational mode of wall movements. For this purpose, a small scale 1 g physical model study was conducted. The experimental setup simulated the conditions of a backfill behind a laterally translating vertical retaining wall in plane strain conditions. To monitor the influence of dilative behavior on failure surface geometry, model tests were conducted on backfills with different densities corresponding to different dilation angles. Failure surface geometries were identified using particle image velocimetry (PIV) method. Friction and dilation angles of the backfill are calculated as functions of failure stress state and relative density of the backfill using a well-known empirical equation, making it possible to quantify the influence of dilation angle on failure surface geometry. As a result, an empirical equation is proposed to predict active failure surface geometry for cohesionless backfills based on peak dilatancy angle. It is shown that the failure surface geometries calculated using the proposed equation are in good agreement with the identified failure surfaces.

• Journal of Institute of Control, Robotics and Systems
• /
• v.15 no.11
• /
• pp.1080-1087
• /
• 2009

This paper presents an algorithm to acquire 3D geometric information using a virtual plane method. The method to measure 3D information on the plane is easy, because it's not concerning value on the z-axis. A plane can be made by arbitrary three points in the 3D space, so the algorithm is able to make a number of virtual planes from feature points on the target object. In this case, these geometric relations between the origin of each virtual plane and the origin of the target object coordinates should be expressed as known homogeneous matrices. To include this idea, the algorithm could induce simple matrix formula which is only concerning unknown geometric relation between the origin of target object and the origin of camera coordinates. Therefore, it's more fast and simple than other methods. For achieving the proposed method, a regular pin-hole camera model and a perspective projection matrix which is defined by a geometric relation between each coordinate system is used. In the final part of this paper, we demonstrate the techniques for a variety of applications, including measurements in industrial parts and known patches images.