• Journal of Dental Rehabilitation and Applied Science
• /
• v.30 no.2
• /
• pp.93-101
• /
• 2014

Purpose: The aim of this study is to investigate the typical shape of the curve of Spee in Korean and analyze the curve of Spee according to gender, age, and left and right. Materials and Methods: Among the patient of Wonkwang University Sanbon Dental Hospital taking cone beam computerized tomography, the images of 500 Koreans (311 males and 189 females) who qualifies the criteria of this study were selected and their curve of Spee were analysed in sagittal plane. Results: The mean radius of curve of Spee in Korean was 91.4 mm. There was statistically significant difference between male (94.6 mm) and female (86.1 mm) by gender, but not significant differences by age and between right and left side. Conclusion: Within the limitation of this study, the smaller radius (91.4 mm) of Korean than the 4-inch (101.6 mm) value advocated by Monson was meaned that it would be need to reconsider the application of the curve of Spee in all cases when occlusal plane is reconstructed in Korean.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.885-899
• /
• 2013

In this paper, we study null helices, null slant helices and Cartan slant helices in $\mathb{E}^3_1$. Using some associated curves, we characterize the null helices and the Cartan slant helices and construct them. Also, we study a space-like curve with the principal normal vector field which is a degenerate plane curve.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.537-544
• /
• 1996

Crofton's formula on Euclidean plane $E^2$ states: Let $\Gamma$ be a rectifiable curve of length L and let G be a straight line. Then $$ \int_{G \cap \Gamma \neq \phi} n dG = 2L $$ where n is the number of the intersection points of G with the curve $\Gamma$.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.849-866
• /
• 2024

In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.

• Journal of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.69-86
• /
• 2017

The point $P{\in}{\mathbb{P}}^2$ is referred to as a Galois point for a nonsingular plane algebraic curve C if the projection ${\pi}_P:C{\rightarrow}{\mathbb{P}}^1$ from P is a Galois covering. In contrast, the point $P^{\prime}{\in}C^{\prime}$ is referred to as a weak Galois Weierstrass point of a nonsingular algebraic curve C' if P' is a Weierstrass point of C' and a total ramification point of some Galois covering $f:C^{\prime}{\rightarrow}{\mathbb{P}}^1$. In this paper, we discuss the following phenomena. For a nonsingular plane curve C with a Galois point P and a double covering ${\varphi}:C{\rightarrow}C^{\prime}$, if there exists a common ramification point of ${\pi}_P$ and ${\varphi}$, then there exists a weak Galois Weierstrass point $P^{\prime}{\in}C^{\prime}$ with its Weierstrass semigroup such that H(P') = or , which is a semigroup generated by two positive integers r and 2r + 1 or 2r - 1, such that P' is a branch point of ${\varphi}$. Conversely, for a weak Galois Weierstrass point $P^{\prime}{\in}C^{\prime}$ with H(P') = or , there exists a nonsingular plane curve C with a Galois point P and a double covering ${\varphi}:C{\rightarrow}C^{\prime}$ such that P' is a branch point of ${\varphi}$.

• Communications of the Korean Mathematical Society
• /
• v.22 no.1
• /
• pp.121-122
• /
• 2007

• Communications of the Korean Mathematical Society
• /
• v.1 no.1
• /
• pp.71-79
• /
• 1986

• Journal of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.281-295
• /
• 1992

• Journal of the Korean Mathematical Society
• /
• v.30 no.2
• /
• pp.385-397
• /
• 1993

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.56 no.1
• /
• pp.188-196
• /
• 2007

In this paper we propose an efficient offset curve generation algorithm for open and closed 2D point sequence curve(PS curve) with line segments in the plane. One of the most difficult problems of offset generation is the loop intersection problem caused by the interference of offset curve segments. We propose an algorithm which removes global as well as local intersection loop without making an intermediate offset curve by forward tracing of tangential circle. Experiment in computer sewing machine shows that proposed method is very useful and simple.