# Parametric representation of a Spiral

• DorumonSg
In summary, to propose a parametric representation of a spiral, you can use the parametric representation of a circle and make the radius variable without introducing a new parameter. For a three-dimensional spiral, a "helix", you can add a "z" component that increases along with the variable radius.
DorumonSg
Propose a parametric representation of a spiral.
Hint: Use the parametric representation of a circle.

This is the parametric representation of a circle we are given :

x = r * Cos(Theta)
y = r * Sin (Theta)

0 <= Theta <= 2 Pi

Nope, we are not given anything background on spirals.

I am like super new at this graphics thingy. I've been searching around the net for 4 hours now, I did find a few answers but none taught me how to get the representation from a circle and I have no idea how they derive at the answer.

x and y are like coordinates.

And that t or Theta in this case is kinda like a path or timeline where decides when coordinates of x and y starts and ends.

I am thinking of making the radius a parameter and then slowly increasing it?

x = u * Cos(Theta)
y = u * Sin (Theta)

1 <= u <= 4

Something like that?

Thats all I know, so help please?

Last edited:
that would work as a 2D spiral, but you would want it all in terms of one parameter, so try starting with theta(u) = u

DorumonSg said:
Propose a parametric representation of a spiral.
Hint: Use the parametric representation of a circle.

This is the parametric representation of a circle we are given :

x = r * Cos(Theta)
y = r * Sin (Theta)

0 <= Theta <= 2 Pi

Nope, we are not given anything background on spirals.

I am like super new at this graphics thingy. I've been searching around the net for 4 hours now, I did find a few answers but none taught me how to get the representation from a circle and I have no idea how they derive at the answer.

x and y are like coordinates.

And that t or Theta in this case is kinda like a path or timeline where decides when coordinates of x and y starts and ends.

I am thinking of making the radius a parameter and then slowly increasing it?

x = u * Cos(Theta)
y = u * Sin (Theta)

1 <= u <= 4

Something like that?
If u is fixed, that is a circle of radius u, not a spiral. If u is a variable, then you have two parameters and that is a surface, not a spiral.

To get a spiral in two dimensions, you need to make the radius variable but not introduce a new variable so something like x= theta*cos(theta), y= theta* sin(theta).

If the problem is, as lanedance suggests, a three dimensional spiral, a "helix", then you need to introduce a "z" component that increases, again not introducing a new parameter.

Something like x= Cos(Theta), y= Sin(Theta), z= Theta.

Thats all I know, so help please?

## 1. What is a parametric representation of a spiral?

A parametric representation of a spiral is a mathematical equation that describes the coordinates of points on a spiral curve. It uses one or more parameters to define the position of each point along the curve.

## 2. Why is a parametric representation used for spirals?

A parametric representation is used for spirals because it allows for more flexibility in defining the shape and size of the spiral. It also allows for easier manipulation and calculation of points on the curve.

## 3. How is a parametric representation of a spiral different from a Cartesian representation?

In a Cartesian representation, the coordinates of points are defined by their distance from the x and y axes. In a parametric representation, the coordinates are defined by parameters, which can be any variable or function. This allows for more complex and varied shapes, such as spirals.

## 4. What are some common parametric equations for spiral curves?

Some common parametric equations for spiral curves include the Archimedean spiral (r = aθ), the logarithmic spiral (r = ab^θ), and the hyperbolic spiral (r = a/θ).

## 5. How are parametric equations for spiral curves used in real life?

Parametric equations for spiral curves are used in many real-life applications, such as designing spiral staircases, creating spiral patterns in art and architecture, and modeling natural phenomena like the spiral shape of galaxies. They are also used in engineering and physics for calculating and predicting the movements of objects in spiraling motion.

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