# circular helix

## circular helix

[′sər·kyə·lər ′hē‚liks]
(mathematics)
A curve that lies on a right circular cylinder and intersects all the elements of the cylinder at the same angle.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Now we show that [alpha](t) is a circular helix in [E.sup.2n+1.sub.v].
So, we can say that [alpha] (t) is a circular helix.
It is easy to show that the curve [alpha](t) is the circular helix.
If both [kappa] and [tau] are non-zero constants, it is called a circular helix.
Hence a circular helix is a Bertrand curve (see [7]).
The circular helix characteristic to the reference worm is the helix corresponding to the reference cylinder and is named the mean circular reference helix of the worm; it has the pitch [p.sub.E] and the inclination [[theta].sub.0] having the size:
The right line d is inclined posed towards the basic cylinder with the angle [[theta].sub.b] that is the inclination angle of the circular helix described by the right line d on the base cylinder.
So, a W-curve of rank 1 is a straight line, a W-curve of rank 2 is a circle, and a W-curve of rank 3 is a right circular helix.
If k and r are positive constants along C, then C is called a circular helix with respect to the Frenet frame.
C is a circular helix with respect to the Frenet frame {[partial derivative]/[partial derivative]v, n, b}, if and only if
In that sense, at the generation of the helical cylindrical surfaces where the theoretic directrix curve D is a circular helix, it is used the composition of a rotation movement with the rectilinear translation movement of the generating element in order to generate a helical circular trajectory in conditions of cinematic correlation (Sandu & Strajescu, 2004), (Botez, 1967).
that represent the known parametric equations of the circular helix and in which

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