Solving a 2D Parametric Plot of Logarithmic Spiral

In summary, a 2D Parametric Plot of Logarithmic Spiral is a graph that represents a spiral curve based on a mathematical equation known as a parametric equation. To solve it, one must determine the values of the parameters in the equation and plot them on a graph. Its purpose is to visualize and analyze the behavior of logarithmic functions, and it has applications in various fields of study. However, it has limitations, such as only representing the spiral in two dimensions and being affected by errors in determining the parameters.
  • #1
izzy93
35
0
I am stuck on the following task;

Create a 2D Parametric Plot showing a spiral path. The parametric equations for a logarithmic spiral are x=k^u Cosine(u), y=k^u Sine(u), where k is a constant, and u is the plot parameter. What does the value of k determine?

I have been typing in the following but it is wrong

ParametricPlot[{(k^u)*(Cos) /. {k -> 1}}, {(k^u)*(Sin) /. {k ->
1}}, {u, 0, 6 Pi}]
Can anyone help?

much appreciated
 
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  • #2
No worries peeps, I figured it out, just had some dodgy brackets about!
 

1. What is a 2D Parametric Plot of Logarithmic Spiral?

A 2D Parametric Plot of Logarithmic Spiral is a graph that represents a spiral curve based on a mathematical equation known as a parametric equation. In this case, the spiral is formed by a logarithmic function, which means that the distance between each turn of the spiral gets progressively larger.

2. How do you solve a 2D Parametric Plot of Logarithmic Spiral?

To solve a 2D Parametric Plot of Logarithmic Spiral, you need to first determine the values of the parameters in the equation. These parameters include the angle of rotation, the distance between each turn, and the starting point of the spiral. Once these values are determined, you can plot the points on a graph and connect them to form the spiral curve.

3. What is the purpose of a 2D Parametric Plot of Logarithmic Spiral?

A 2D Parametric Plot of Logarithmic Spiral is used to visualize and analyze the behavior of logarithmic functions in a two-dimensional space. It can be used to understand how the parameters in the equation affect the shape of the spiral and to compare different equations that produce logarithmic spirals.

4. What are the applications of a 2D Parametric Plot of Logarithmic Spiral?

A 2D Parametric Plot of Logarithmic Spiral has various applications in mathematics and science. It is used in fields such as physics, engineering, and biology to model and analyze natural phenomena that follow logarithmic patterns, such as the growth of certain organisms or the decay of radioactive materials.

5. Are there any limitations to using a 2D Parametric Plot of Logarithmic Spiral?

One limitation of a 2D Parametric Plot of Logarithmic Spiral is that it only represents the spiral in a two-dimensional space. In reality, many natural phenomena that follow logarithmic patterns exist in three-dimensional spaces. Additionally, the accuracy of the plot depends on the accuracy of the parameters used in the equation, so any errors in determining these values can affect the results.

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