• Journal for History of Mathematics
• /
• v.34 no.1
• /
• pp.1-20
• /
• 2021

Logic and intuition are considered as the opposite extremes of teaching geometry, and any teaching method of geometry is to be placed between these extremes. The purpose of this study is to identify the characteristics of logical and intuitive approaches for teaching geometry and to derive didactical implications by taking Euclid's Elements and Clairaut's Elements respectively representing the extremes. To this end, comparing the composition and contents of each book, we analyze which propositions Clairaut chose from Euclid's Elements, how their approaches differ in definitions, proofs, and geometrical constructions, and what unique approaches Clairaut took. The results reveal that Clairaut mainly chose propositions from Euclid's books 1, 3, 6, 11, and 12 to provide the contexts that show why such ideas were needed, rather than the sudden appearance of abstract and formal propositions, and omitted or modified the process of justification according to learners' levels. These propose a variety of intuitive strategies in line with trends of teaching geometry towards emphasis on conceptual understanding and different levels of justification. Specifically, such as the general principle of similarity and the infinite geometric approach shown in Clairaut's Elements, we could confirm that intuition-based geometry does not necessarily aim for tasks with low cognitive demand, but must be taught in a way that learners can understand.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.9 no.6
• /
• pp.2132-2143
• /
• 2015

This paper presents two distance geometry-based algorithms for wireless location in cellular network systems-distance geometry filtering (DGF) and distance geometry constraint (DGC). With time-of-arrival range measurements, the DGF algorithm estimates the mobile station position by selecting a set of measurements with relatively small NLOS (non-line-of-sight) errors, and the DGC algorithm optimizes the measurements first and then estimates the position using those optimized measurements. Simulation results show that the proposed algorithms can mitigate the impact of NLOS errors and effectively improve the accuracy of wireless location.

• Proceedings of the KSRS Conference
• /
• 2005.10a
• /
• pp.182-185
• /
• 2005

Satellite cameras are calibrated before launch in detail and in general, but it cannot be guaranteed that the geometry is not changing during launch and caused by thermal influence of the sun in the orbit. Modem satellite imaging systems are based on CCD-line sensors. Because of the required high sampling rate the length of used CCD-lines is limited. For reaching a sufficient swath width, some CCD-lines are combined to a longer virtual CCD-line. The images generated by the individual CCD-lines do overlap slightly and so they can be shifted in x- and y-direction in relation to a chosen reference image just based on tie points. For the alignment and difference in scale, control points are required. The resulting virtual image has only negligible errors in areas with very large difference in height caused by the difference in the location of the projection centers. Color images can be related to the joint panchromatic scenes just based on tie points. Pan-sharpened images may show only small color shifts in very mountainous areas and for moving objects. The direct sensor orientation has to be calibrated based on control points. Discrepancies in horizontal shift can only be separated from attitude discrepancies with a good three-dimensional control point distribution. For such a calibration a program based on geometric reconstruction of the sensor orientation is required. The approximations by 3D-affine transformation or direct linear transformation (DL n cannot be used. These methods do have also disadvantages for standard sensor orientation. The image orientation by geometric reconstruction can be improved by self calibration with additional parameters for the analysis and compensation of remaining systematic effects for example caused by a not linear CCD-line. The determined sensor geometry can be used for the generation? of rational polynomial coefficients, describing the sensor geometry by relations of polynomials of the ground coordinates X, Y and Z.

• Transactions of Materials Processing
• /
• v.5 no.2
• /
• pp.165-175
• /
• 1996

the process of strip twisting is practiced for the manufacture of some commercial parts such as elements for tube type line mixers. A thin metal strip with rectangular cross section is twisted thru an angle greater than 180。. Initial geometry is altered in to a complex one with dimen-sional changes. In practice several tryouts are necessary to obtain required dimensional accu-racies. A simple analysis model is proposed to predict the dimensional changes forming torque and axial force.

• 제어로봇시스템학회:학술대회논문집
• /
• 2002.10a
• /
• pp.34.4-34
• /
• 2002

1. Introduction 2. Basic Camera models and geometry 3. Projection of line widths 4. Camera calibration algorithm 5. Experimental results 6. Conclusions and future work

• Journal of the Korean Institute of Intelligent Systems
• /
• v.14 no.4
• /
• pp.506-511
• /
• 2004

Biometrics is getting more and more attention in recent years for security and other concerns. So far, only fingerprint recognition has seen limited success for on-line security check, since other biometrics verification and identification systems require more complicated and expensive acquisition interfaces and recognition processes. Hand-Geometry has been used for biometric verification and identification because of its acquisition convenience and good performance for verification and identification performance. Hence, it can be a good candidate for online checks. Therefore, this paper proposes a Hand-Geometry recognition system based on geometrical features of hand. From anatomical point of view, human hand can be characterized by its length, width, thickness, geometrical composition, shapes of the palm, and shape and geometry of the fingers. This paper proposes thirty relevant features for a Hand-Geometry recognition system. However, during experimentation, it was discovered that length measured from the tip of the finger was not a reliable feature. Hence, we propose a new technique based on Genetic Algorithm for extraction of the center of nail bottom, in order to use it for the length feature.

• Journal of Korean Society for Geospatial Information Science
• /
• v.15 no.4
• /
• pp.81-88
• /
• 2007

The geometry of satellite image captured by linear CCD sensor is different from that of frame camera image. The fact that the exterior orientation parameters for satellite image with linear CCD sensor varies from scan line by scan line, causes the difference of image geometry between frame and linear CCD sensor. Therefore, we need the epipolar geometry for linear CCD image which differs from that of frame camera image. In this paper, we proposed a method of resampling linear CCD satellite image in epipolar geometry under the assumption that image is not formed in perspective projection but in parallel projection, and the sensor model is a 2D affine sensor model based on parallel projection. For the experiment, IKONOS stereo images, which are high resolution linear CCD images, were used and tested. As results, the spatial accuracy of 2D affine sensor model is investigated and the accuracy of epipolar resampled image with RFM was presented.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.150.4-150
• /
• 2001

The geometry PIG provides pipeline operators with continuous measurement of pipe centerline coordinates, bend radius, displacement, and bending strain in a single pass through the pipeline. This study introduces the developed geometry PIG(Pipeline Inspection Gauge) which is used for geometry surveys. This tool is equipped with the several sensor systems. The Inertial Navigation System (INS) comprises angle rate gyros and linear accelerometers. The system measures the precise path of the PIG during its traverse of the pipeline. This system is also used to produce a detailed map of the lire, measure curvature. Odometers measure the PIG´s distance moved along the line and instantaneous speed during the PIG run. Caliper sensors measure pipeline ...

• Journal of The Korean Astronomical Society
• /
• v.46 no.3
• /
• pp.97-102
• /
• 2013

In the present work, we prove the validity of two theorems on null-paths in a version of absolute parallelismgeometry. A version of these theorems has been originally established and proved by Kermak, McCrea and Whittaker (KMW) in the context of Riemannian geometry. The importance of such theorems lies in their applications to derive a general formula for the redshift of spectral lines coming from distant objects. The formula derived in the present work can be applied to both cosmological and astrophysical redshifts. It takes into account the shifts resulting from gravitation, different motions of the source of photons, spin of the moving particle (photons) and the direction of the line of sight. It is shown that this formula cannot be derived in the context of Riemannian geometry, but it can be reduced to a formula given by KMW under certain conditions.

• Journal for History of Mathematics
• /
• v.32 no.1
• /
• pp.17-25
• /
• 2019

This essay elucidates the way the geometries of space-time theories explain material bodies' motions. A conventional attempt to interpret the way that space-time geometry explains is to consider the geometrical structure of space-time as involving a causally efficient entity that directs material bodies to follow their trajectories corresponding to the laws of motion. Newtonian substantival space is interpreted as an entity that acts but is not acted on by the motions of material bodies. And Einstein's curved space-time is interpreted as an entity that causes the motions of bodies. This essay argues against this line of thought and provides an alternative understanding of the way space-time geometry explain the laws of motion. The workings of the way that Newton's flat and Einstein's curved space-time explains the law of motion is such that space-time geometry encodes the principle of inertia which specifies straight lines of moving bodies.