in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

a method has been presented for finding the solution surface of the npde: u  c , bounded by a general space curve. the method is based on the geometric characteristics of the surface, and is called the “cone-slot method”. it has been shown that such a surface can be obtained by movement of a cone inside the slot formed by the boundary space curve. an algorithm has been suggested on the basis ...

In mathematics classes where the natural numbers are studied, several surprising results can be shown about the relative “sizes” of infinite sets, such as the fact the there is a oneto-one mapping between the natural numbers N and the even numbers, showing that they are both countably infinite, with the “same size”. Similar logic also shows that there is a mapping from the natural numbers N ont...

In mathematics classes where the natural numbers are studied, several surprising results can be shown about the relative “sizes” of infinite sets, such as the fact the there is a oneto-one mapping between the natural numbers N and the even numbers, showing that they are both countably infinite, with the “same size”. Similar logic also shows that there is a mapping from the natural numbers N ont...

Hilbert’s two-dimensional space-filling curve is appreciated for its good locality-preserving properties and easy implementation for many applications. However, Hilbert did not describe how to generalize his construction to higher dimensions. In fact, the number of ways in which this may be done ranges from zero to infinite, depending on what properties of the Hilbert curve one considers

We introduce Peano words, which are words corresponding to finite approximations of the Peano space filling curve. We then find the number of occurrences of certain patterns in these words.

v. dannon showed that spherical curves in e4 can be given by frenet-like equations, and he thengave an integral characterization for spherical curves in e4 . in this paper, lorentzian spherical timelike andspacelike curves in the space time 41 r are shown to be given by frenet-like equations of timelike andspacelike curves in the euclidean space e3 and the minkowski 3-space 31 r . thus, finding...

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...