• School Mathematics
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• v.3 no.1
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• pp.25-44
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• 2001

The purpose of the study is to investigate multifaced aspects of angle concepts and the developments of angle concept and to examine textbooks in relation to above investigation. In this study, we obtain the following results. First, angle concepts have static and dynamic aspects and develop situated angle concepts, contextual angle concepts, abstract angle concepts, through formal angle concepts. Second, our textbooks emphasize abstract angle concepts and formal angle concepts but lack situated angle concepts and contextual angle concepts.

• East Asian mathematical journal
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• v.26 no.2
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• pp.115-140
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• 2010

The purpose of this paper was to develop manipulative materials to teach the angle concepts and construct a teaching-learning program by using that. Furthermore, this study analyzed how does the program affect students understanding of the angle concepts. To check the effects of learning activities with manipulative materials on the understanding of an angle concepts, applied observation during class and write a mathematics journal writing, a description of students impressions at the end of the class and analyzed before and after test paper. We find that students approached the subject more friendly and knew well about the mathematical concepts by using materials. Furthermore, this activity helped that way to solve add and subtract of the angle, estimate ability, round angle concept, positive response in mathematics learning.

• Education of Primary School Mathematics
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• v.21 no.2
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• pp.209-221
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• 2018

Angle concepts have a multifaceted nature such as quantitative aspects as the amount of rotation, qualitative aspects as geometric shapes, and relationship aspects made with planes or lines. This study analysed angle concepts and introduction methods of angles in elementary mathematics textbooks which have been used from the Syllabus Period to the 2015 Revised Mathematics Curriculum. First, the concepts of angles in mathematics textbooks focus through the definitions, representations, and components of angles presented in mathematics textbooks are analyzed. Secondly, how various aspects of each angle are sequenced through the tasks or activties in the introduction of lesson is looked. As a result of analysis, the methods of introducing angles in the changes of mathematics textbooks have mainly focused on learning about geometric shapes and relations of components. In the mathematics classroom, students should experience various aspects of geometric shapes, rotations, relational aspects of points, lines and surfaces, and support and link them to form a wide range of concepts.

• The Mathematical Education
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• v.6 no.2
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• pp.1-9
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• 1968

In mathematics, a definition must have authentic reasons to be defined so. On defining geometric figures, there must be adequencies in sequel and consistency in the concepts of figures, though the dimensions of them are different. So we can avoid complicated thoughts from the study of geometric property. From the texts of SMSG, UICSM and others, we can find easily that the same concepts are not kept up on defining some figures such as ray and segment on a line, angle and polygon on a plane, and polyhedral angle and polyhedron on a 3-dimensionl space. And the measure of angle is not well-defined on basis of measure theory. Moreover, the concepts for interior, exterior, and frontier of each figure used in these texts are different from those of general topology and algebraic topology. To avoid such absurdness, I myself made new terms and their definitions, such as 'gan' instead of angle, 'polygonal region' instead of polygon, and 'polyhedral solid' instead of polyhedron, where each new figure contains its interior. The scope of this work is hmited to the fundamental idea, and it merely has dealt with on the concepts of measure, dimension, and topological property. In this case, the measure of a figure is a set function of it, so the concepts of measure is coincided with that of measure theory, and we can deduce the topological property for it from abstract stage. It also presents appropriate concepts required in much clearer fashion than traditional method.

• The Mathematical Education
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• v.62 no.1
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• pp.79-93
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• 2023

This study used metaphors as a analysis tool to investigate elementary school students' formation and development of angle concepts. For this purpose, the students were asked to write words associated with angle, right angle, acute angle and obtuse angle and to explain why. In case of angle and right angle, responses of 268 students from 3rd to 6th graders were analyzed and for acute angle and obtuse angle, those of 192 students from 4th to 6th graders were examined. As the results of categorizing the metaphors, they can be classified into categories such as; (1) qualitative aspects: 'things metaphor', 'personality metaphor', 'emotions metaphor' etc., (2) quantitative aspects: 'motions metaphor', 'changes metaphor', 'emotions metaphor' etc., and (3) relational aspects: 'shape relations metaphor.' The metaphoric expressions were prominent in 'qualitative aspects' associated with shapes. As for the other aspects, 'quantitative aspect'- the size of angles and the amount of spread and 'relational aspects' - elements of angle and relationship with another shapes, the frequency increses were shown to as grade levels were up. In case of right angle and acute angle, 'qualitative aspects' associated with shapes were outstanding and the frequency of the metaphoric expressions of obtuse angle was distributed similarly in three aspects. As the figure strand and the measurement strand are integrated to an strand in the 2022 revised curriculum, we need more discussion of multifaced aspects of angle and the learning sequences in the 'figure and measurement' strand.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.6
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• pp.647-655
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• 1999

For linear time-varying systems described by the triple (A(t),B(t),C(t)) where A(t),B(t),C(t) are the system, the input, and the output matrices, respectively, we propose concepts for measures of modal and gross controllability /observability. We introduce a differential algebraic eigenbvalue theory for linear time-varying systems to calculate the PD-eigenvalues and left and right PD-eigenvectors of the system matrix A(t) which will be used to derive the concepts for the measures. The time-dependent angle between the left PD-eigenvectors of the system matrix A(t) and the columns of the input matrix B(t), and the magnitude of the each element of the input matrix B(t) are used to propose the modal controllability measure. Similarly, the time-dependent angle between the right PD-eigenvectors of the system matrix A(t) and the rows of the output matrix C(t) are used to propose the madal observability measure. Gross measure of controllability of a mode from all inputs and its gross measure of observability in all outputs for the linear time-varying systems are also proposed. Numerical examples are presented to illustrate the proposed concepts.

• Journal of Power System Engineering
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• v.14 no.3
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• pp.39-45
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• 2010

The dynamic stability of a robot vehicle can be enhanced by the Force-Angle Stability Margin concept that considers a variety of dynamic effects. To evaluate the robot vehicle stability, a SPI(stability performance index), which is a function of the suspension arm angles, was used. If the SPI has a minimum value, the robot vehicle has maximum stability. The FASM and SPI concepts were incorporated in the mobility simulation by using ADAMS and MATLAB/Simulink. The simulation results using these concepts showed significant improvements of the vehicle stability on rough terrains.

• Science of Emotion and Sensibility
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• v.5 no.3
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• pp.67-74
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• 2002

Testing device was newly designed and built to measure the dynamic contact angle. The measurement was made using microscope interfaced with computerized image analysis system while the dynamic condition being controled using Instron. As specimens for the experiment, two different types of fibers, i.e., hydrophilic and hydrophobic, were prepared. In case of hydrophilic fiber, the increase of twist level gave the increase of contact angle. However, in hydrophobic yarn the increase of twist level gave the decrease of contact angle. When saline was used as a telling liquid, the increase of the concentration gave the increase of contact angle. The results rationalized clearly on the basis of known concepts could be used in designing fabric structure for the improvement of comport performance.

• Communications of Mathematical Education
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• v.21 no.3
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• pp.515-525
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• 2007

In this study, we study on equations of bisector and trisectors of angle. We analyze various studies related with bisector and trisectors of angle. As a result we have known that trisectors of angle is able to received by paper folding method. Using some concepts of vector we have described equations of bisector and trisectors of angle.

• Proceedings of the Korean Fiber Society Conference
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• 1997.04a
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• pp.127-133
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• 1997

Authors measured the apparent contact angle in a yarn using microscope because it gives a useful information in the evaluation of comfort factors in fabrics. The mechanical stage of microscope was designed and built to facilitate this measurement. Variables examined were the fiber type, the twisting number, and the fluid type. All produced significant effect most of which could be rationalized based on the known concepts. The methodology used and the results obtained are discussed in detail.