• Journal of Korea Multimedia Society
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• v.9 no.2
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• pp.234-243
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• 2006

The recent rapid development of HCI and surveillance technologies has brought great interests in application systems to process faces. Much of research efforts in these systems has been primarily focused on such areas as face recognition, facial expression analysis and facial feature extraction. However, not many approaches have been reported toward face direction detection. This paper proposes a method to detect the direction of a face using a facial feature called facial triangle, which is formed by two eyebrows and the lower lip. Specifically, based on the single monocular view of the face, the proposed method introduces very simple formulas to estimate the horizontal or vertical rotation angle of the face. The horizontal rotation angle can be calculated by using a ratio between the areas of left and right facial triangles, while the vertical angle can be obtained from a ratio between the base and height of facial triangle. Experimental results showed that our method makes it possible to obtain the horizontal angle within an error tolerance of ${\pm}1.68^{\circ}$, and that it performs better as the magnitude of the vertical rotation angle increases.

• Education of Primary School Mathematics
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• v.20 no.4
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• pp.305-319
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• 2017

In the process of finding the triangle height, 26 students in the 6th grade were surveyed to understand the students' triangle height through the eye movement data and to investigate the cognitive load of the students. As a result, the correctness rate of the pre-test was significantly increased in the post-test, and the frequency and retention of gaze data were smaller in the post-test than in the AOI of each question. The Participants's subjective cognitive load indicated that it was more difficult to understand the concept of rotated triangles compared with upright triangles that were parallel to the ground. More frequent and more retentions in the eye-tracking data were detected in the right triangles and acute triangles by rotating configuration. Eye movement data show that eye tracking technology can provide an objective measure of students' cognitive load for feedback on instructional design.

• Journal for History of Mathematics
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• v.15 no.1
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• pp.43-56
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• 2002

Hong, Jung-Ha(1684-\ulcorner ) explained 78 problems which look for the length of right triangle satisfying the given conditions by the Pythagorean theorem or the ratio of similarity in the chapter ‘Goo-Go-Hoh-Eun-Moon’of the 5th volume of his book Goo-Ill-Jeep. Most questions are formulated by equations of degree 2, 3, 4 which mostly have rational number solutions and part of the equations are expressed by counting stick. The explanation of each question describes the procedure to make the equation in detail, but only presents the solution with a few steps to solve.

• Journal for History of Mathematics
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• v.12 no.1
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• pp.13-20
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• 1999

Lee, Sang-Hyuk(1810-\ulcorner) explained application problems which can be represented as the equation of degree 1 or 2 in the chapter of 'Myun-Lyu' of his book 'Cha-Geun-Bang-Mong-Gu.' Mainly he dealt with the various questions which looks for the length of right triangle and square. After they are expressed in the equation, all of them has terms on both side of equality sign and they have solution as integer. The explanation of each question describes the procedure to make the equation in detail, but only presents the solution with few step to solve.

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.121-127
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• 1999

We can get the Pascal's matrix of order n by taking the first n rows of Pascal's triangle and filling in with 0's on the right. In this paper we obtain some well known combinatorial identities and a factorization of the Stirling matrix from the Pascal's matrix.

• East Asian mathematical journal
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• v.28 no.4
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• pp.419-433
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• 2012

In this paper, by using the inductive method, recurrence relation, the unit circle, circle to inscribe a right-angled triangle, formula of multiple angles, solution of quadratic equation and Fibonacci numbers, we study various problem solving methods to find pythagorean triple.

• Imaging Science in Dentistry
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• v.31 no.3
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• pp.175-179
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• 2001

Cystic lymphangioma is an uncommon benign developmental tumor of the lymphatic system, seen rarely in adults. A 23-year-old man visited DKUDH complaining of the painless swelling in the right submandibular area. It was reported that swelling had increased since 5 months ago. Clinically, fltriangle uctuant and mobile mass was palpated at the right submandibular area. CT scan showed a large, well-defined, homogenous low density mass, measuring 5.0 × 2.5 × 4.0 cm. T1W MRI scan demonstrated a large, multiseptated homogenous low signal mass with septum and rim enhancement. Proton-density and T2W MRI scan showed mass of high signal intensity. MRI scan was able to delineate better the enhanced multi septation and extent of the lesion. Histopathologically, a lobulated cystic mass lined by a layer of flattened endothelium was observed.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.23 no.1
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• pp.159-164
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• 1993

Cystic hygroma is a special form of lymphangioma. It most often occurs in the neck of children. We observed a 14-year-old male whose chief complaint was a abnormal swelling of the right mandibular angle area. The computerized tomography showed the well-defined nonenhancing cystic mass on right submandibular gland area and anterior triangle of the neck. The histopathologic fidings exhibited the multiloculatedfluid-filled cysts, which are lined a flattened layer of endothelial cells with foci of lymphocytes found lying adjacent to the lining. After evaluation of above findings, the mass was diagnosed as a cystic hygroma in the neck.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.161-169
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• 2021

The two-dimensional confusion matrix used in credit assessment, biostatistics, and many other fields consists of true positive, true negative, false positive, and false negative. Their rates, such as the true positive rate (TPR), true negative rate (TNR), false positive rate, and false negative rate, can be applied to measure its accuracy. In this study, we propose the TPR-TNR plot, a graphical method that can geometrically describe and explain these rates based on the confusion matrix. The proposed TPR-TNR plot consists of two right-angled triangles. We obtain that the TPR and TNR describe the acute angles of right-angled triangles in the plot. These acute angles can be used to determine optimal thresholds corresponding to lots of accuracy measures.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.21 no.10
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• pp.1177-1183
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• 2010

In this paper, design of a microstrip-fed, Spidron fractal-shaped slot antenna with circular polarization is represented. The ground plane of the designed antenna has a slot that comprises seven right-angled triangle next to each other in a low. A reflector is placed at the bottom on microstrip feeding line to enhance the antenna gain. The optimized design was conducted by varying a length of the first right-angled triangle, location of feeding line, space between a substrate and a reflector. The proposed antenna was fabricated on a Taconic-RF35 substrate. The entire dimension of the fabricated antenna is $40{\times}40{\times}18.6mm^3$ and the reflector is 18.6 mm away from the ground plane. The measured gain of the fabricated antenna is 6.7 dBi at 4.3 GHz. The measured bandwidths of -10 dB reflection and 3 dB axial ratio are 41 % and 7.4 %, respectively.