Kartionkierteisiä

Kartionkierteisiä, sometimes referred to as conical helix or conoid helix, describes a three-dimensional curve that winds around a cone. Unlike a standard helix which winds around a cylinder, a kartionkierteisiä maintains a constant angle with respect to the axis of the cone. This means that as the curve progresses along the cone's surface, its distance from the cone's axis changes, increasing or decreasing depending on whether the cone is opening or closing.

The mathematical description of a kartionkierteisiä can be expressed in cylindrical coordinates (r, θ, z) as follows: r = aθ and z = bθ, where 'a' and 'b' are constants that determine the shape and pitch of the helix. Alternatively, in spherical coordinates (ρ, θ, φ), it can be represented as ρ = cθ and φ = constant, where 'c' is a constant related to the cone's apex angle. The parameter θ represents the angle of rotation.

Visually, a kartionkierteisiä can be imagined by taking a standard helix and stretching or compressing it along its axis. This results in a curve that either spirals outwards or inwards as it ascends or descends the cone. Examples of where this type of curve might appear include certain natural formations, decorative architectural elements, or in theoretical physics and mathematics. The concept is a generalization of the cylindrical helix to a conical surface.