• Journal of Educational Research in Mathematics
• /
• v.15 no.2
• /
• pp.131-145
• /
• 2005

This study intends to analyze didactically on triangle-determining conditions and triangle-congruence conditions. The result of this study revealed the followings: Firstly, many pre-service mathematics teachers and secondary school students have insufficient understanding or misunderstanding on triangle-determining conditions and triangle-congruence conditions. Secondly, the term segment instead of edge may show well the concern of triangle-determining conditions. Thirdly, when students learn the method of finding six elements of triangle using the law of sines and cosines in high school, they should be given the opportunity to reflect the relation and the difference between triangle-determining situation and the situation of finding six elements of triangle. Fourthly, accepting some conditions like SSA-obtuse as a triangle-determining condition or not is not just a logical problem. It depends on the specific contexts investigating triangle-determining conditions. Fifthly, textbooks and classroom teaching need to guide students to discover triangle-deter-mining conditions in the process of inquiry from SSS, SSA, SAS, SAA, ASS, ASA, AAS, AAA to SSS, SAS, ASA, SAA. Sixthly, it is necessary to have students know the significance of 'correspondence' in congruence conditions. Finally, there are some problems of using the term 'correspondent' in describing triangle-congruence conditions.

• Restorative Dentistry and Endodontics
• /
• v.7 no.1
• /
• pp.53-57
• /
• 1981

A total of 130 extracted human maxillary second molars were used to study the configuration of the floor of the pulp chamber. The specimens were ground and the pulp chamber was examined with a magnifier and explored with sharp explorer. The study showed the shape of the pulp chamber, number of root canals, and the type of canal orifice. The results were as follows; 1. In so far as observing the shape of the pulp chamber of the teeth, 16.9% of the teeth were quadrilateral, 70.0% were triangle and 13.1% were ovoid shape. 2. 13.1% of the specimens have 4 root canal orifices. 73.9% have 3 root canal orifices, 11.5% have 2 root canal orifices and 1.5% have single orifice. 3. 13.1% of the specimens have 2 mesio-buccal canal orifices and among the teeth those have 3 canals, 20.8% show 'Y' shape, 29.1% show straight line and 23.8% show obtuse triangle shape.

• Education of Primary School Mathematics
• /
• v.20 no.2
• /
• pp.163-175
• /
• 2017

The purpose of the study is to identify the effect of length and right angle indication on the understanding of the concept of the figure when presenting the task of classifying the plane figures. we recorded thirty three 4th grade students' performance with eye-tracking technologies and analyzed the correct answer rate and gaze duration. The findings from the study were as follows. First, correctness rate increased and Gaze duration decreased by marking length in isosceles triangle and equilateral triangle. Second, correctness rate increased and Gaze duration decreased by marking right angle in acute angle triangle and obtuse triangle. Based on these results, it is necessary to focus on measuring the understanding of the concept of the figure rather than measuring the students' ability to measure by expressing the length and angle when presenting the task of classifying the plane figures.

• Education of Primary School Mathematics
• /
• v.18 no.1
• /
• pp.45-59
• /
• 2015

This study focused on the classification of triangles by angles in elementary school mathematics. We examined Korean national mathematics curriculum from the past to the present. We also examined foreign textbooks and the Euclid's . As a result, it showed that the classification is not indispensable from the mathematical and the perceptual viewpoint. It is rather useful for students to know the names of triangles when studying upper level mathematics in middle and high schools. This study also suggested that the classification be introduced in elementary school mathematics in the context of reasoning and inquiring as shown foreign textbooks, and example topics for the reasoning and inquiring.

• School Mathematics
• /
• v.4 no.2
• /
• pp.283-296
• /
• 2002

In this study we tried to find the method of using the tangrams and the mosaic puzzles together for learning the elementary geometry in the Korean primary schools. The tangram and the mosaic puzzle activity-panels were developed and the activity-cards for them also were designed. The criteria to be used for the analyses of contents of the activity-cards were developed. We surveyed and analyzed the students' responses, A previous research had insisted that solely using the tangrams were not useful in learning about an obtuse-angled triangle in the elementary geometry (Welchman, 1999), but the combinative uses of the tangrams and the mosaic puzzles were found to extend the limits of the previous study in investigating the figures of the plain diagrams. Actually, the tangrams and the mosaic puzzles helped the students to learn the concepts of several elements of the plain diagrams such as 'angles', 'sides', and 'angular points', with students'operational comparison of the diagrams developed with them. They also provided useful clues in learning the relationship between the 'length' and the 'area' of the Plain diagrams. The students participated in the class with much activities, using the operational learning materials. They also comprehended the concepts and the principles of the elementary geometry more thoroughly, expressing their ideas in spoken or written languages through interactive communication. In conclusion, the tangram and mosaic puzzles can be used for learning the elementary geometry of the primary school level as motivative learning materials, helping students enhance diverse mathematical thinking and discover mathematical principles.

• Journal of the Korean Institute of Traditional Landscape Architecture
• /
• v.28 no.3
• /
• pp.72-84
• /
• 2010

This study was attempted in order to offer basic data for implementing and applying Samjonseokjo(三尊石造), which is one of traditional stone construction method, by confirming how the constructive principle is expressed such as proportional beauty, which is contained in the modeling of Triad of Buddha Carved on Rock that was formed in the period of the Three States, centering on Triad of Buddha Carved on Rock in Susan. The summarized findings are as follows. 1. As a result of analyzing size and proportion of totally 17 of Triad of Buddha Carved on Rock, the average total height in Bonjonbul(本尊佛) was 2.96m. Right Hyeopsi(右挾侍) was 2.19m. Left Hyeopsi(左挾侍) was 2.16m. The height ratio according to this was 100:75:75, thereby having shown the relationship of left-right symmetrical balance. The area ratio in left-right Hyeopsi was 13.4:13.7, thereby the two area having been evenly matched. 2. The Triad of Buddha Carved on Rock in Seosan is carved on Inam(印岩) rock after crossing over Sambulgyo bridge of the Yonghyeon valley. Left direction was measured with $S47^{\circ}E$ in an angle of direction. This is judged to target an image change and an aesthetic sense in a Buddhist statue according to direction of sunlight while blocking worshipers' dazzling. 3. As for iconic characteristics of Buddha Carved on Rock in Seosan, there is even Hyeopsi in Bangasang(半跏像) and Bongjiboju(捧持寶珠) type Bosangipsang. In the face of Samjon composition in left-right asymmetry, the unification is indicated while the same line and shape are repeated. Thus, the stably visual balance is being shown. 4. In case of Triad of Buddha Carved on Rock in Seosan, total height in Bonjonbul, left Hyeopsi, and right Hyeopsi was 2.80m, 1.66m, and 1.70m, respectively. Height ratio in left-right Hyeopsibul was 0.60:0.62, thereby having been almost equal. On the other hand, the area ratio was 28.8:25.2, thereby having shown bigger difference. The area ratio on a plane was grasped to come closer to Samjae aesthetic proportion. 5. The axial angle of centering on Gwangbae was 84:46:50, thereby having been close to right angle. On the other hand, the axial angle ratio of centering on Yeonhwajwa(蓮華坐: lotus position) was measured to be 135:25:20, thereby having shown the form of inequilateral triangle close to obtuse angle. Accordingly, the upper part and the lower part of Triad of Buddha Carved on Rock in Susan are taking the stably proportional sense in the middle of maintaining the corresponding relationship through angular proportion of inequilateral triangle in right angle and obtuse angle. 6. The distance ratio in the upper half was 0.51:0.36:0.38. On the other hand, the distance ratio in the lower half was 0.53 : 0.33 : 0.27. Thus, the up-down and left-right symmetrical balance is being formed while showing the image closer to inequilateral triangle. 7. As a result of examining relationship of Samjae-mi(三才美) targeting Triad of Buddha Carved on Rock in Susan, the angular ratio was shown to be more notable that forms the area ratio or triangular form rather than length ratio. The inequilateral triangle, which is formed centering on Gwangbae(光背) in the upper part and Yeonhwajwa(lotus position) in the lower part, is becoming very importantly internal motive of doubling the constructive beauty among Samjae, no less than the mutually height and area ratio in Samjonbul.