• Journal for History of Mathematics
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• v.19 no.1
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• pp.79-90
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• 2006

The purpose of this paper is to derive the ratios of trigonometric special angles from Euclid's by constructing regular pentagon and decagon. The intention of this paper is started from recognizing that teaching of the special angles in secondary math classroom excessively depends on algebraic approaches rather geometric approaches which are the origin of the trigonometric ratios. In this paper the method of constructing regular pentagon and decagon is reviewed and the geometric relationship between this construction and trigonometric special angles is derived. Through such geometric approach the meaning of trigonometric special angles is analyzed from a geometric perspective and pedagogical ideas of teaching these trigonometric ratios is suggested using history of mathematics.

• International Journal of Highway Engineering
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• v.17 no.6
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• pp.33-36
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• 2015

PURPOSES : It is desirable for buses to be parallel to the face of the bus shelter at a bus stop. In this way, passengers can safely use the buses without moving into the vehicle area. The study was a review of the current bus bay geometric guidelines, to determine whether they lead buses to stop parallel to the face of the bus shelter by analyzing vehicle trajectory. METHODS : A commercial software program for vehicle trajectory analysis was used under our assumptions about bus dimensions and geometric values. The final position of the bus was analyzed for multiple trajectory simulations, reflecting various geometric alternatives. RESULTS : Within the scope of the study, we concluded that the current design guidelines need to be revised by the design values suggested by the study. CONCLUSIONS : The results of the study suggested alternative design values for bus bay geometry, based on the assumption that buses should be parallel to the face of the bus shelter in order to prevent passengers from moving into the vehicle area.

• Journal of Korean Society of Occupational and Environmental Hygiene
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• v.27 no.1
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• pp.46-58
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• 2017

Objectives: Particulate matter (PM) at construction sites mostly originates from either construction activities or the atmospheric environment. This study was conducted to evaluate the exposure level to PM and the contribution ratio of atmosphere sources at construction sites. Methods: We reviewed literature and governmental systems related to PM exposure in occupational settings and summarized them. In the field evaluation, five construction sites and one golf course were selected: two from Gyeonggi-do Province and four from North Gyeongsang-do Province. For each site, personal samples from outdoor construction workers and area samples from the outdoor area around the construction site office were collected according to construction work types. PM concentrations reported from nearby National Ambient Air Monitoring Stations were recorded. Respirable dust concentrations, respirable silica concentrations, and several metal concentrations including Cd, Cr, Pb, and As were monitored over four months. In the end we suggested how to manage particulate matter exposure at construction sites. Results: There was little literature reporting on exposure levels of construction workers to PM. Respirable dust concentrations measured in Gyeonggi-do Province were higher than those measured in North Gyeongsang-do Province. The geometric means of respirable dust concentrations in personal samples and area samples were $37.89{\mu}g/m^3$ and $92.86{\mu}g/m^3$, respectively. The respirable dust concentrations were higher than the PM concentrations reported from nearby National Ambient Air Monitoring Station. The geometric means of respirable silica concentrations of personal samples and area samples were $1.3{\mu}g/m^3$ and $1.1{\mu}g/m^3$, respectively. All metal concentrations were lower than 10% of individual Korean occupational exposure limits. Conclusions: Assuming that personal samples consisted of ambient PM and dust originating from work activities and area samples only collected ambient PM, we concluded that the dust exposure of outdoor construction workers originated 40.8% from the atmosphere and 59.2% from construction activities. PM exposure at construction sites should be controlled by employers, as in the case of outdoor heat stress. The Korean government needs to consider setting an occupational exposure limit for respirable dust.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.361-366
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• 2009

In this paper we consider constructive function triples on the real numbers $\mathbb{R}$ and on (not necessarily commutative) integral domains D which permit the construction of a multitude of d-algebras via these constructive function triples. At the same time these constructions permit one to consider various conditions on these d-algebras for subsets of solutions of various equations, thereby producing geometric problems and interesting visualizations of some of these subsets of solutions. In particular, one may consider what notions such as "locally BCK" ought to mean, certainly in the setting provided below.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.4
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• pp.211-224
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• 2010

We define some asset models which are useful for portfolio construction in various terms of time. Our asset models are geometric jump-diffusions defined by the solutions of stochastic differential equations which are decomposed by various terms of time basically. We also can study pricing and hedging strategy of options in our models roughly.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.267-298
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• 1999

A geometric construction of an exact algebraic formula for graded partition functions, of which a special one is the classical unrestricted partition function p(n), from a diophantine point of view is presented. Moreover, the involved process allows us to compute the value of a graded partition function in an inductive manner with a geometrically built-in self-error-checking ability at each step for correctness of the computed values of the partition function under consideration.

• Proceedings of the Korean Institute of Building Construction Conference
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• 2014.11a
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• pp.100-101
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• 2014

The generation of 3D models for freeform buildings is an important task while continuous monitoring of the related spatial information at different time phases. Realistic models of freeform building have to provide high geometric accuracy and detail at an effective data size.(Al-kheder, S. 2008) The efficiency of this image-based technique has been increased considerably by the development of digital technologies. Furthermore, 3D data collection based on laser scanning has become an high quality 3D models for construction site. Therefore, in this research, we have an effort to review construction methods to make freeform envelope of building using 3D scanning technology.

• International conference on construction engineering and project management
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• 2015.10a
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• pp.537-539
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• 2015

considerate operation is a major issue in the equipment-intensive operation. Identifying an optimal equipment combination is important to achieve low-energy operations. An Earthwork operation planning system, which measures the energy consumption of construction operations by taking into account construction equipments' engineering attributes (e.g., weight, capacity, energy consumption rate, etc.) and operation conditions (e.g., road condition, attributes of materials to be moved, geometric information, etc.), is essential to achieve the low-energy consumption. This study develops an automated computerized system which identifies an optimal earthmoving equipment fleet minimizing the energy consumption. The system imports a standard template of earthmoving operation model and compares numerous scenarios using alternative equipment allocation plans. It finds the fleet that minimizes the energy consumption by enumerating all cases using sensitivity analysis. A case study is presented to verify the validity of the system.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.13-26
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• 2011

The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles's Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students' geometric levels using the van Hieles's theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles's geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

• International conference on construction engineering and project management
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• 2013.01a
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• pp.1-6
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• 2013

Concrete construction requires utilization of many temporary facilities such as formwork, shoring, and scaffolding. Appropriate use of these temporary facilities greatly impacts the quality, cost, schedule, and safety of concrete construction. The current practice in design and planning of temporary facilities is often manual, error-prone, and re-active based on construction site layout, status, and progress in the field. Early design and planning of temporary facilities for concrete construction using Building Information Modeling (BIM) technology offers a potential solution. Although some commercially-available software exists that assists in the generation of temporary facility designs, the construction industry lacks tools that support detailed planning and design of many other temporary facilities. This research presents our early work in automating the design and planning of temporary facilities utilizing BIM. Algorithms were developed to automatically assess geometric conditions of work space to detect required temporary facilities and design them. The proposed methodology was implemented in a test model. By automatically incorporating temporary facilities into BIM, more realistic construction models can be created with less effort and errors. Temporary facilities-loaded models can finally be used for communication, bill of materials, scheduling, etc. and as a benchmark for field installation of temporary formwork, shoring, and scaffolding systems.