• Journal of Power System Engineering
• /
• v.13 no.2
• /
• pp.30-35
• /
• 2009

Numerical Calculations for dimensionless pressure drop (friction factor times Reynolds number) have been obtained for fully developed laminar flow of MPL(Modified Power Law) fluid in isosceles triangle pipes. The solutions are valid for Pseudoplastic fluids over a wide range from Newtonian behavior at low shear rates through transition region to power law behavior at higher shear rates. The analysis identified a dimensionless shear rate parameter which for a given set of operating conditions specifies where in the shear rate range a particular system is operating, i.e., Newtonian, transition or power law region. The numerical calculation data of the dimensionless pressure drop for the Newtonian and power law regions are compared with previously published asymptotic results presenting within 0.16 % in Newtonian region and 2.98 % in power law region.

• Journal for History of Mathematics
• /
• v.17 no.3
• /
• pp.93-108
• /
• 2004

In this article we study on various proofs of the Steiner-Lehmus theorem(any triangle that has two equal angle bisectors is isosceles). We suggest 6 geometric proofs and 3 algebraic proofs of the theorem in detail, analyze these proofs, extract related theorems, proof ideas.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.2 no.1
• /
• pp.54-64
• /
• 1984

This paper is a study on structural measurement by using a terrestrial camera. The aim of this paper is to understand the method of a composition by analyzing the geometrical compositive ratio of threestoried pagodas at Gamun-Sa, Gosun-Sa, Bulguk-Sa, Seated iron Buddha in Kwang-Jn, and Main-Seat Buddha at Sukkuram Cave-temple. Measured data and contour maps are accurately obtained by means of photogrammetry, and the following points are able to he found by analyzing them. At first, for Stone Pagodas. the breaths of the Okgesuks are made to the ratio, 8 : 7 : 6. And when an equililateral triangle and an 45$^{\circ}$ isosceles triangle are drawn of which the bases are the length of the upper Gabsuk, and then a circle is drawn whose radius is the length between the vertexes of the two triangles and its center is the vertex of the former the circle passes the upper line of the third Oksin. Also it can be found that an $70^{\circ}$ isosceles triangle being drawn at base line, the triangle passes the edge point of the upper Gabsuk and the center of the third Okgesuk. Also for Budha statues, it can be found that circles whose center is that of eyes can be drawn, and if 2 lines which pass the shoulder and the center of Buddha's body are extended, they intersect the knees.

• East Asian mathematical journal
• /
• v.31 no.4
• /
• pp.459-481
• /
• 2015

In this study, we investigated whether the theorem is established even if we replace a 'square' element in the Euclidean proof of the Pythagorean theorem with different figures. At this time, we used different figures as equilateral, isosceles triangle, (mutant) a right triangle, a rectangle, a parallelogram, and any similar figures. Pythagorean theorem implies a relationship between the three sides of a right triangle. However, the procedure of Euclidean proof is discussed in relation between the areas of the square, which each edge is the length of each side of a right triangle. In this study, according to the attached figures, we found that the Pythagorean theorem appears in the following three cases, that is, the relationship between the sides, the relationship between the areas, and one case that do not appear in the previous two cases directly. In addition, we recognized the efficiency of Euclidean proof attached the square. This proving activity requires a mathematical process, and a generalization of this process is a good material that can experience the diversity and rigor at the same time.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.5
• /
• pp.1597-1617
• /
• 2017

The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them Sharygin triangles. It turns out that they are parametrized by an open subset of an elliptic curve. Also we prove that there are infinitely many non-similar integer Sharygin triangles.

• Journal of applied mathematics & informatics
• /
• v.11 no.1_2
• /
• pp.125-141
• /
• 2003

This paper treats the conditions for the existence and stability properties of stationary solutions of reaction-diffusion equations of Gierer-Meinhardt type, subject to Neumann boundary data. The domains in which diffusion takes place are of three types: a regular hexagon, a rectangle and an isosceles rectangular triangle. Considering one of the relevant features of the domains as a bifurcation parameter it will be shown that at a certain critical value a diffusion driven instability occurs and Turing bifurcation takes place: a pattern emerges.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.4 no.4
• /
• pp.95-103
• /
• 1984

This paper is a study on improving the accuracy of control points by suggesting angular requirements which make geometric conditions to be optimum. For this purpose, a equation, by which the accuracy of control point coordinates measured in an arbitrary station can be estimated, is derived. This equation is integrated and average standard error of the coordinates is computed, so that the optimum location of observatory station is determined. In the case of triangulation, a regular triangle has been generally considered as the best geometric condition, but because the precision of each side is different, the $52.77^{\circ}$ isosceles triangle is founded to be the best one. Also in trigonometric leveling, the geometric condition is founded to be optimum when the base angle of a isosceles triangle is $45^{\circ}$. In control surveying for close-range photogrammetry the optimum relation between base length($B_0$) and object distance($D_0$) can be founded to be as follow; $D_0=0.357587-0.357967B_0+0.308555B_0{^2}$.

• Archives of Plastic Surgery
• /
• v.42 no.2
• /
• pp.226-231
• /
• 2015

The aim of this study is to consider breast imagery in art as depicted through western painting. Twenty western art paintings were collated. Most of the sample paintings were created from the mid-nineteenth century to the late twentieth century and some are from the Renaissance period. Ten anthropometric items were used to measure 15 distances between two landmarks and 3 angles between three points. The distance from the nipple to the sternal notch and to the midclavicular point was the same and they were 0.46 of the distance from the sternal notch to the umbilicus. The shape of the projection of the breast was almost an isosceles triangle and the altitude of the triangle was at a proportion of 0.45 of the bottom length and 0.16 of the distance from the sternal notch to the umbilicus. The distance between the lateral ends of the breasts was 2.14 times the facial width and the distance between nipples was 1.36 times the facial width. Proportions from works of art are more ideal and attractive than clinically measured proportions. The desirable ratios measured from historical paintings might be useful in planning breast surgeries.

• Journal for History of Mathematics
• /
• v.22 no.4
• /
• pp.41-52
• /
• 2009

This study investigates a mathematical subject, 'triangles' in mathematics books of Chosun Dynasty, in special Muk Sa Jib San Bub(默思集算法), Gu Il Jib(九一集), San Hak Ib Mun(算學入門), Ju Hae Su Yong(籌解需用), and San Sul Gwan Gyun(算術管見). It is likely that they apt to avoid manipulating general triangles except the right triangles and the isosceles triangles etc. Our investigation says that the progress of triangle-related contents in Chosun mathematics can fall into three stages: measurement of the triangle-shaped fields, transition from the object of measurement to the object of geometrical study, and examination of definition, properties and validation influenced by western mathematics.