• Journal of Educational Research in Mathematics
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• v.14 no.2
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• pp.171-185
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• 2004

Students are exposed to a concept of tangent from a specific context of the relation between a circle and straight lines at the 7th grade. This initial experience might cause epistemological obstacles regarding learning concepts of tangent to additional curves. The paper provides a method of how to introduce a series of concepts of tangent in order to lead students to revise and improve the concept of tangent which they have. As students have chance to reflect and revise a series of concepts of tangent step by step, they realize the facts that the properties such as 'meeting the curve at one point' and 'touching but not cutting the curve' may be regarded as the proper definition of tangent in some limited contexts but are not essential in more general contexts. And finally students can grasp and appreciate that concept of tangent as the limit of secants and the relation between tangent and derivative.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.6
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• pp.499-505
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• 2017

In this study, the limit loads calculated by the $m_{\alpha}-tangent$ method based on the linear finite element analysis are compared with the closed form solutions that are proposed by various authors. The objects of the analysis is to select the elbow and the branch pipe which are representative structure of piping system. The applicability of the $m_{\alpha}-tangent$ method are investigated by applying it to cases with various geometries. The internal pressure and the in-plane bending moment are considered and the $m_{\alpha}-tangent$ method is in good agreement with the existing solutions in case of elbows. However, the limit loads calculated by the $m_{\alpha}-tangent$ method for branch junctions do not agree well with the existing solutions and do not show any tendency. The reason is a biased result due to the stress concentration of the discontinuous parts.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.575-584
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• 2006

In this paper we introduce a discrete tangent vector of a polygon defined on each vertex by a linear combination of forward difference and backward difference, and show that if the polygon is originated from a smooth curve then direction of the discrete tangent vector is a second order approximation of the direction of the tangent vector of the original curve. Using this discrete tangent vector, we also introduced the geometric cubic Hermite interpolation of a polygon with controlled initial and terminal speed of the curve segments proportional to the edge length. In this case the whole interpolation is $C^1$. Experiments suggest that about $90\%$ of the edge length is the best fit for the initial and terminal speeds.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.753-763
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• 2023

In this paper, we introduce a fully modified (p, q)-poly tangent polynomials and numbers of the first type. We investigate analytic properties that is related with (p, q)-Gaussian binomial coefficients. We also define (p, q)-Stirling numbers of the second kind and fully modified (p, q)-poly tangent polynomials and numbers of the first type with two variables. Moreover, we derive some identities are concerned with the modified tangent polynomials and the (p, q)-Stirling numbers.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.625-642
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• 2009

In the school mathematics the concept of tangent is introduced in several steps in suitable contexts. Students are required to reflect and revise their concepts of tangent in order to apply the improved concept to wider range of contexts. In this paper we consider the tangent as the optimal linear approximation to a curve at a given point and make three discussions on pedagogical aspects of it. First, it provides a method of finding roots of real numbers which can be used as an application of tangent. This may help students improve their affective variables such as interest, attitude, motivation about the learning of tangent. Second, this concept reflects the modern point of view of tangent, the linear approximation of nonlinear problems. Third, it gives precise meaning of two tangent lines appearing two sides of a cusp point of a curve.

• Honam Mathematical Journal
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• v.38 no.2
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• pp.375-384
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• 2016

In this paper, we study the pseudo-symmetry of unit tangent sphere bundle. We prove that if the unit tangent sphere bundle $T_1M$ with standard contact metric structure over a locally symmetric $M^n$, $n{\geq}3$ is pseudo-symmetric, then M is of constant curvature.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.29-34
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• 2014

Almost contact and almost complex structures in the tangent bundle have been studied by K. Yano and S. Ishihara[5] and others. In the present paper, we have studied Lorentzian almost r-para-contact structure in the tangent bundle. Some results related to Lie-derivative have been studied.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1255-1267
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• 2020

The class of isotropic almost complex structures, J_𝛿,𝜎, define a class of Riemannian metrics, g_𝛿,𝜎, on the tangent bundle of a Riemannian manifold which are a generalization of the Sasaki metric. This paper characterizes the metrics g_𝛿,0 using the geometry of tangent bundle. As a by-product, some integrability results will be reported for J_𝛿,𝜎.

• 한국전산유체공학회:학술대회논문집
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• 2007.04a
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• pp.3-7
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• 2007

The characteristics of asymmetric vortex and side force of tangent-ogive-cylinder flight vehicle at high angles of attack have been performed by using upwind Navier-Stokes method with the ${\kappa}-{\omega}$ turbulence model. And Asymmetric transition positions are considered for generation of asymmetric vortex.

• Kyungpook Mathematical Journal
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• v.63 no.1
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• pp.79-95
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• 2023

In this note, we define a Berger type deformed Sasaki metric as a natural metric on the second tangent bundle of a manifold by means of a biparacomplex structure. First, we obtain the Levi-Civita connection of this metric. Secondly, we get the curvature tensor, sectional curvature, and scalar curvature. Afterwards, we obtain some formulas characterizing the geodesics with respect to the metric on the second tangent bundle. Finally, we present the harmonicity conditions for some maps.