• Journal for History of Mathematics
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• v.33 no.3
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• pp.155-165
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• 2020

Pythagorean theorem is a proposition on the relationship between the lengths of three sides of a right triangle. It is well known that Pythagorean theorem for Euclidean geometry deforms into an interesting form in non-Euclidean geometry. In this paper, we investigate a new perspective that replaces right triangles with 'proper triangles' so that Pythagorean theorem extends to non-Euclidean geometries without any modification. This is seen from the perspective that a rectangle is an equiangular quadrilateral, and a right triangle is a half of a rectangle. Surprisingly, a proper triangle (defined by Paolo Maraner), which is a half of an equiangular quadrilateral, satisfies Pythagorean theorem in many geometries, including hyperbolic geometry and spherical geometry.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.22 no.5
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• pp.322-327
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• 2010

It is a critical task to keep the ventilation system working in a proper and efficient manner in large multi-storey buildings, and the enthalpy exchanger is becoming an increasingly important part of the ventilation system by playing the function of channeling heat and moisture. We present a computational study on the heat transfer performance of the cross-flow enthalpy exchanger, which is in large use for residential buildings. The ducts are considered whose cross-sectional shapes resemble triangle and longitudinal centerline a cosine wave. It is shown that, as the cross-sectional shape departs from triangle, the heat transfer performance of the duct tends to deteriorate. Also, applying the wave-like shape to the longitudinal centerline of the duct increases the rate of heat transfer and the applied pressure-gradient at the same time. The origin of the performance variations in the cases considered are quantitatively analyzed and discussed.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.8 no.3
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• pp.35-41
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• 1999

STL which is used in Rapid Prototyping is composed of a lot of triangular facets. The number of triangles and the shapes of these triangles determine the quality of STL. Therefore, proper algorithm is necessary to enhance the quality of triangular patch. In this paper we used the Delaunay triangulation method to apply to following processes. 1) On processing for reducing sharp triangles which cause errors on intersection. 2) On processing for connecting two or more collinear edges. 3) On processing for deleting unnecessarily inserted points in coplanar polygon.

• Smart Structures and Systems
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• v.13 no.4
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• pp.547-565
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• 2014

This paper investigates the design of a perfect point load actuator based on flat triangular piezoelectric patches. Applying a difference of electric potential between the electrodes of a triangular patch leads to point loads at the tips and distributed moments along the edges of the electrodes. The previously derived analytical expressions of these forces show that they depend on two factors: the width over height (b/l) ratio of the triangle, and the ratio of the in-plane piezoelectric properties ($e_{31}/e_{32}$) of the active layer of the piezoelectric patch. In this paper, it is shown that by a proper choice of b/l and of the piezoelectric properties, the moments can be cancelled, so that if one side of the triangle is clamped, a perfect point load actuation can be achieved. This requires $e_{31}/e_{32}$ to be negative, which imposes the use of interdigitated electrodes instead of continuous ones. The design of two transducers with interdigitated electrodes for perfect point load actuation on a clamped plate is verified with finite element calculations. The first design is based on a full piezoelectric ceramic patch and shows superior actuation performance than the second design based on a piezocomposite patch with a volume fraction of fibres of 86%. The results show that both designs lead to perfect point load actuation while the use of an isotropic PZT patch with continuous electrodes gives significantly different results.

• Progress in Superconductivity and Cryogenics
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• v.10 no.3
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• pp.5-8
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• 2008

On highly-textured IBAD-MgO templates, we have tried to find proper buffer layers among various candidate materials, including $LaMnO_3$ (LMO), $La_2Zr_2O_7$ (LAO), $LaAlO_3$ (LAO), $LaGaO_3$ (LGO), $NdGaO_3$ (NGO), and $BaZrO_3$ (BZO). All buffer layers were deposited on the IBAD-MgO templates by KrF pulsed laser deposition(PLD). LAO layer showed an armorphous phase. LZO, LGO, and NGO layers showed polycrystalline growth. Only LMO and BZO layers exhibited c-axis oriented biaxially textured films. Optimally processed LMO buffer layer at deposition temperature of $750^{\circ}C$ and $PO_2$ of 100mTorr exhibited ${\triangle}{\phi}$ value of ${\sim}-5.2^{\circ}$ and RMS roughness of 5.6nm. Interestingly, BZO buffer layers with ${\triangle}{\phi}$ values of ${\sim}-6^{\circ}$ could be routinely produced over a wide PLD processing condition.

• Journal of the Korean Dietetic Association
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• v.9 no.4
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• pp.307-315
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• 2003

This study was to investigate the relation of nutrients intake, health status, and bone mineral density in middle-aged women. Daily nutrients intake were analyzed by convenient method. The BMD of subjects were measured by Dual Energy X-ray Absorptiometry(DEXA). BMD was measured at the spine(vertebrae L2-L4) and femur(neck, Ward's triangle and trochanter). The nutrients intake of subjects were higher than recommended dietary allowances(RDA) except for calorie, iron, calcium, vitamin B1. Nutrients intake of vitamin A(p<0.05), iron(p<0.01), vitamin $B_2$(p<0.05), niacin(p<0.05), and vitamin C(p<0.05) between $\leq$49 yr group and $\geq$50 yr group. Mean daily intake of calcium was much less than the Korean RDA, 78.5% in $\leq$49 yr group and 77.3% in $\geq$50 yr group. 35.8% of the subjects under 50 years of age($\leq$49 yr group) and 77.4% of the subjects from 50 years up($\geq$50 yr group) were classified as osteopenia or osteoporosis. BMD of L2-L4 were positively correlated with height(p<0.05), weight(p<0.05) and BMI(p<0.05). BMD of femoral neck was positively correlated with BMI(p<0.05), BMD of Ward's triangle was positively correlated with weight(p<0.001). But BMD of L2-L4 and femoral neck were negatively correlated with age(p<0.05), menarche(p<0.05). BMD of Ward's triangle was negatively correlated with age(p<0.001). The BMD of L2-L4 were positively correlated with animal protein(p<0.05), calcium(p<0.05) and iron(p<0.05). The BMD of femoral neck was positively correlated with animal protein(p<0.05). The BMD of Ward's triangle was positively correlated with animal protein(p<0.001) and iron(p<0.001). The above results suggest that it should be difficult to prevent middle-aged women's bone destruction through nutrients intake. Further investigation is necessary to prove the mutual relations between BMD, exercise, and calcium intake. Therefore, middle-aged women will need proper exercise as well as Ca supplementation in order to prevent osteoporosis with aging.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1998.03a
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• pp.129-134
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• 1998

STL which is used in Rapid Prototyping is composed of a lot of triangular facets. The number of triangles and the shapes of these triangles determine the quality of STL. Therefore, proper algorithm is necessary to enhance the quality of triangular patch. In this paper we used the Delaunay triangulation method to apply to following processes. 1) On processing for reducing sharp triangles which cause errors on intersection. 2) On processing for connecting two or more collinear edges. 3) On processing for deleting unnecessarily inserted points in coplanar polygon.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.185-191
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• 2004

Given a connected graph G, we say that a set EC\;{\subseteq}\;V(G)$ is convex in G if, for every pair of vertices x, $y\;{\in}\;C$, the vertex set of every x - y geodesic in G is contained in C. The convexity number of G is the cardinality of a maximal proper convex set in G. In this paper, we show that every pair k, n of integers with $2\;{\leq}k\;{\leq}\;n\;-\;1$ is realizable as the convexity number and order, respectively, of some connected triangle-free graph, and give a lower bound for the convexity number of k-regular graphs of order n with n > k+1.

• Journal for History of Mathematics
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• v.16 no.2
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• pp.55-70
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• 2003

This study investigated tile intuitive level of justification in geometry, as the former step to the aximatization, with concrete examples. First, we analyze limitations that the axiomatic method has in tile context of discovery and the educational situation. This limitations can be supplemented by the proper use of the intuitive method. Then, using the histo-genetic analysis, this study shows the process of the development of geometrical thought consists of experimental, intuitive, and axiomatic steps. The intuitive method of proof which is free from the rigorous axiom has an advantage that can include the context of discovery. Finally, this paper presents the issue of intuitive proving that the three angles of an arbitrary triangle amount to 180$^{\circ}$, as an example of the local systematization.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1495-1498
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• 2002

The constrained average method is one of dither methods which combines edge emphasis and grayscale rendition to provide legibility of textual region and proper quality of continuous tone region. How-ever, image quality of continuous tone region is insufficient compared to other dither methods, such as ordered dither methods or the error diffusion method. The constrained average method uses a uniform distribution function to decide number of lit pixels related to the average intensity in a picture area. However, actual distribution of continuous tone region is closer to the Laplacian distribution or triangle distribution. In this paper, we introduce various probability distributions and the actual luminance distribution to decide the threshold value of the constrained average method in order to improve image quality of dithered image.