• Communications of Mathematical Education
• /
• v.21 no.3
• /
• pp.385-406
• /
• 2007

In this paper we study on various properties of triangle's escribed circle and tetrahedron's escribed sphere. In order to accomplish our study we extract some base problems related with investigating these properties. Using the base problems we are able to prove various properties of triangle's escribed circle, and to systemize these properties. And we succeed in drawing an analogy related with tetrahedron's escribed sphere.

• Journal of applied mathematics & informatics
• /
• v.40 no.5_6
• /
• pp.1167-1179
• /
• 2022

In this paper, we obtain some subsets of real numbers (ℝ) on which a fractional part function is defined as a real-valued continuous function. This gives rise to the analysis of the continuous properties of the fractional part function as a real-valued function. The analysis of fractional part function is helpful in the study of the dynamics of circle.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.507-514
• /
• 2023

Suppose that a line passing through a given point P intersects a given circle 𝓒 at Q and R in the Euclidean plane. It is well known that |PQ||P R| is independent of the choice of the line as long as the line meets the circle at two points. It is also known that similar properties hold in the 2-sphere and in the hyperbolic plane. New proofs for the similar properties in the 2-sphere and in the hyperbolic plane are given.

• Communications of Mathematical Education
• /
• v.20 no.1 s.25
• /
• pp.9-18
• /
• 2006

In this paper we study on concept analogy of altitude and escribed circle of triangle. We start from following theorems related with sides of triangle: existence of triangle, Pythagoras theorem, cosine theorem, Heron formula. Using concept analogy of sides-altitudes, altitudes-escribed circle's radii we discover some properties of altitude and escribed circle's radii and prove these properties.

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1115-1122
• /
• 1996

In study of the dynamics of a map f from a topological space X to itself, a central role is played by the various recursive properties of the points of X. One such property is periodicity. A weaker property is that of being nonwandering. Intermediate recursive properties include almost periodicity and recurrence.

• Journal of Forest and Environmental Science
• /
• v.34 no.5
• /
• pp.359-375
• /
• 2018

The long term ecological effects have been reported in natural forest ecosystem due to various anthropogenic disturbances, especially in tropics of the world. The present study was carried out in the sanctuary area of central India to assess the changes on litter biomass, litterfall pattern and soil attributes under different disturbance regimes. The study area includes three forest circles i.e., Bhoramdeo, Jamunpani and Salehwara each comprising three disturbances regimes viz., high, medium and low severity of biotic pressure. A noticeable variation and impact were recorded in different sites. The impact varies significantly from least disturbed sites to highly disturbed sites across the circle and among different disturbances level. The seasonal mean total forest floor biomass across the forest circles varied from 2.18 to $3.30t\;ha^{-1}$. It was found highest under lightly disturbed site and lowest under heavily disturbed site. Total litterfall varied from 5.11 to $7.06t\;ha^{-1}\;yr^{-1}$ across the forest circle. Lowest litterfall was recorded at heavily disturbed site while highest in lightly disturbed site. Annual turnover of litter varied from 69-73% and the turnover time ranged between 1.37-1.45 years. The turn over time was higher for heavily disturbed site and lower for lightly disturbed site. The heavily disturbed site of all the circle showed the sandy loam soil texture, whereas moderately and lightly disturbed site comprised of sandy loam, sandy clay loam and clay soil texture, respectively. The bulk density decreases from heavily disturbed site to lightly disturbed site and the pH of soils ranged from 5.57-6.89 across the circle. Across the circle the total soil nitrogen ranged from 0.12-0.21%, phosphorus from 10.03-24.00 kg and Potassium from $139.88-448.35kg\;ha^{-1}$, respectively. Our results demonstrate that anthropogenic disturbances regime significantly influences forest floors in terms of mass, composition and dynamics along with litterfall rate and soil properties.

• Journal of Digital Convergence
• /
• v.11 no.2
• /
• pp.215-220
• /
• 2013

They are well-known geometric properties of a circle that the perpendicular bisector of a chord passes through the center of a circle, and the intersection of the perpendicular bisectors of any two chords is its center. This paper is related to a fast pupil detection method capable of detecting the center and the radius of a pupil using these geometric properties at high speed when detecting the pupil region for iris segmentation. The proposed method is characterized as rapidly detecting the center and the radius of the pupil, extracting the candidate points of the circle in human eye images using morphological operations, and finding two chords using four points on the circular edge, and taking the intersection of the perpendicular bisectors of these two chords for its center. The proposed method can not only detect the center and the radius of a pupil rapidly but also find partially occluded pupils in human eye images.

• Journal of the Korean School Mathematics Society
• /
• v.21 no.4
• /
• pp.445-467
• /
• 2018

In this study, we analyzed the contents of pi and the area of a circle presented in Korean, Japanese, Singapore, and American mathematics textbooks, and drew implications for the teaching of pi and the area of a circle in school mathematics. We developed a textbook analysis framework by theoretical discussions on the concept of the pi based on the various properties of pi and the area of a circle based on the central ideas of measurement and the previous researches on pi and the area of a circle in elementary mathematics. We drew five suggestions for improving the teaching of pi and three suggestions for improving the teaching of the area of a circle in Korean elementary schools.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10a
• /
• pp.161-167
• /
• 1993

This paper presents robustness properties of the Kalman Filter ad the associated LQG/LTR method for linear time-invariant systems having delays in both the state and output. A circle condition relating to the return difference matrix associated with the Kalman filter is derived. Using this circle condition, it is shown that the Kalman filter guarantees(1/2, .inf.) gain margin and .+-.60.deg. phase margin, which are the same as those for nondelay systems. However, it is shown that, even for minimum phase plants, the LQG/LTR method can not recover the target loop transfer function. Instead, an upper bound on the recovery error is obtained using an upper bound of the solution of the Kalman filter Riccati equations. Finally, some dual properties between output-delated system and input-delayed systems are exploited.

• Communications of Mathematical Education
• /
• v.24 no.1
• /
• pp.195-220
• /
• 2010

The magic square is one of the number arrangements and the sums of each row, column, and diagonal are all equal. The meaning of "方" is "Square". If we don't consider the condition of 'square' then is it possible any number arrangement? There are many special number arrangements such as "magic five number circle(緊五圖)", "magic six number circle(聚六圖)", "magic eight number circle(聚八圖)", "magic nine number circle(攢九圖)", "magic eight camp circle(八陣圖)", "magic nine camp circle(連環圖)" in the ancient Chinese mathematics books such as "楊輝算法", "算法統宗". Also, there is a very special and beautiful number arrangement Jisuguimoondo(地數龜文圖) in the mathematics book "Goosuryak(九數略)" written by Choi suk jung(崔錫鼎) in the Joseon Dynasty. In this study, we introduce a various number arrangements and their properties.