Formula for Spiral Around Cone - Get Your Answer Here

In summary, for a spiral formed around a conical shape, the equation for a "spring-like" spiral with varying height can be described using a parametric equation, such as r(t)=(t sin t, t cos t, t), where t represents time. This equation can be used to visualize a "spring-like" spiral with a height that increases over time.
  • #1
eli_lied
12
0
I am looking for the formula to describe a spiral formed around a conical shape. If any particular details are needed, please make them variables and define them.

Thanks to all for the help!
 
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  • #2
Hi eli_lied! :smile:

Do you mean a shortest-possible-distance spiral, as if a string was pulled tight around the cone?

If so, then remember a cone's "own" geometry (as opposed to embedded geometry) is flat Euclidean …

so just cut the cone along a generator, unfold it, draw a straight line on it, and then join it up again. :wink:
 
  • #3
Thanks for the reply Tiny Tim :)

What I'm specifically looking for is the equation for a "spring-like" spiral that is, for lack of a better term, 0 at one end and infinity at the other. As though a spring were wrapped around a conical formation with a varying height that increases over time.
 
  • #4
The simplest method would be to use a parametric equation

[tex] r(t)=(x(t), y(t), z(t)): x(t)=t \sin t, y(t)=t \cos t, z(t)=t [/tex]

or something like that.
 

What is the formula for finding the spiral around a cone?

The formula for finding the spiral around a cone is 2πr, where r is the radius of the base of the cone.

Why is the formula for the spiral around a cone important?

The formula for the spiral around a cone is important because it allows us to calculate the length of the spiral, which can be useful in various applications such as architecture, engineering, and mathematics.

How is the formula for the spiral around a cone derived?

The formula for the spiral around a cone is derived by using the Pythagorean Theorem to find the hypotenuse of a right triangle formed by the radius of the base and the height of the cone. This hypotenuse represents the length of the spiral around the cone.

Can the formula for the spiral around a cone be used for any type of cone?

Yes, the formula for the spiral around a cone can be used for any type of cone, as long as the base is circular and the height is perpendicular to the base.

What are some practical applications of the formula for the spiral around a cone?

The formula for the spiral around a cone has practical applications in fields such as architecture, engineering, and mathematics. It can be used to determine the length of spiral stairs, the surface area of a cone-shaped tank, and the distance traveled by a point on a rotating cone, among others.

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