Conical Helix
In mathematics, a conical spiral, also known as a conical helix, is a space curve on a right circular cone, whose Orthographic projection, floor projection is a plane spiral. If the floor projection is a logarithmic spiral, it is called ''conchospiral'' (from conch). Parametric representation In the x-y-plane a spiral with parametric representation : x=r(\varphi)\cos\varphi \ ,\qquad y=r(\varphi)\sin\varphi a third coordinate z(\varphi) can be added such that the space curve lies on the cone with equation \;m^2(x^2+y^2)=(z-z_0)^2\ ,\ m>0\; : * x=r(\varphi)\cos\varphi \ ,\qquad y=r(\varphi)\sin\varphi\ , \qquad \color \ . Such curves are called conical spirals. They were known to Pappos. Parameter m is the slope of the cone's lines with respect to the x-y-plane. A conical spiral can instead be seen as the orthogonal projection of the floor plan spiral onto the cone. Examples : 1) Starting with an ''archimedean spiral'' \;r(\varphi)=a\varphi\; gives the conical spiral ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]