Closed Curves and Space Curves
نویسنده
چکیده
So far we have discussed only ‘local’ properties of (plane) curves. These properties depend only on the behavior of a curve near a given point, and not on the ‘global’ shape of the curve. Now let us look at some global results about curves. The most famous, and perhaps the oldest, of these is the ‘isoperimetric inequality’, which relates the length of a certain ‘closed’ curve to the area it contains. Later on, we will discuss space curves with an introduction to the celebrated Frenet formula.
منابع مشابه
Special Bertrand Curves in semi-Euclidean space E4^2 and their Characterizations
In [14] Matsuda and Yorozu.explained that there is no special Bertrand curves in Eⁿ and they new kind of Bertrand curves called (1,3)-type Bertrand curves Euclidean space. In this paper , by using the similar methods given by Matsuda and Yorozu [14], we obtain that bitorsion of the quaternionic curve is not equal to zero in semi-Euclidean space E4^2. Obtain (N,B2) type quaternionic Bertrand cur...
متن کاملTENSION QUARTIC TRIGONOMETRIC BÉZIER CURVES PRESERVING INTERPOLATION CURVES SHAPE
In this paper simple quartic trigonometric polynomial blending functions, with a tensionparameter, are presented. These type of functions are useful for constructing trigonometricB´ezier curves and surfaces, they can be applied to construct continuous shape preservinginterpolation spline curves with shape parameters. To better visualize objects and graphics atension parameter is included. In th...
متن کاملA characterization of curves in Galilean 4-space $G_4$
In the present study, we consider a regular curve in Galilean $4$-space $mathbb{G}_{4}$ whose position vector is written as a linear combination of its Frenet vectors. We characterize such curves in terms of their curvature functions. Further, we obtain some results of rectifying, constant ratio, $T$-constant and $N$-constant curves in $mathbb{G}_{4}$.
متن کاملOn the Quaternionic Curves in the Semi-Euclidean Space E_4_2
In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.
متن کاملThe Physics of Time Travel
TIME travel has traditionally been the domain of science fiction, not physics. Fortunately, however, at least within Einstein's theories of relativity, discussions of time travel are open to physicists as well. Special relativity unifies the concepts of time and space. General relativity goes beyond unification and allows time and space to warp together in the presence of matter. General relati...
متن کامل