Can I visualize three variable functions through scalar and vector fields?

  • Thread starter LucasGB
  • Start date
181
0
Graphics of one variable functions are two dimensional lines. Graphics of two variable functions are three dimensional surfaces. Three variable functions cannot be plotted.

But can I think of the usual 3D representations of vector and scalar fields as manners of visualizing a three variable function?
 
In fact, a scalar field IS a scalar function and likewise a vector field IS a vector function, so a representation of a 3D scalar field is in fact a representation of a 3 variable scalar function.

Any 3D representations of a 3D scalar or vector field on a 2D plane like your computer screen or a sheet of paper cannot be a continuous plot however, only some finite amount of points will be represented like the one in here:

http://upload.wikimedia.org/wikipedia/commons/d/d1/Vector_Field.gif

In the image above, the magnitude of each vector is represented by adding a colour dimension to the 3 spatial dimensions
 

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top