The Osculating Plane of a Space Curve - Synthetic Formulations
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Parallel Transport Frame in 4 -dimensional Euclidean Space
In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The conditi...
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At every point, a smooth plane curve can be approximated, to second order, by a circle; this circle is called osculating. One may think of the osculating circle as passing through three infinitesimally close points of the curve. A vertex of the curve is a point at which the osculating circle hyper-osculates: it approximates the curve to third order. Equivalently, a vertex is a critical point of...
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At every point, a smooth plane curve can be approximated, to second order, by a circle; this circle is called osculating. One may think of the osculating circle as passing through three infinitesimally close points of the curve. A vertex of the curve is a point at which the osculating circle hyper-osculates: it approximates the curve to third order. Equivalently, a vertex is a critical point of...
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At every point, a smooth plane curve can be approximated, to second order, by a circle; this circle is called osculating. One may think of the osculating circle as passing through three infinitesimally close points of the curve. A vertex of the curve is a point at which the osculating circle hyper-osculates: it approximates the curve to third order. Equivalently, a vertex is a critical point of...
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تاریخ انتشار 1998