Can Physics Equations Be Visualized as Geometric Shapes?

[thedy]

Hi,I m thinking about,what is dimension meaning in physics.Is it any analogy with square or cube,for example?Let have for example the simplest example,distance:s=v*t.Can I draw this equation like rectangle object?Like in geometry,we have for rectangle equation a*b,now we have v*t.I know,it is totally non-sense question,but I m interesting in it.
Does physicists use this view on stuff?
Thanks

 

[chiro]

Hey thedy and welcome to the forums.

Typically a dimension in things like physics, engineering, and science (as opposed to mathematics) concerns the ratio of sets of units. In general you have a ratio of two units and those units are basically made up of multiplying other sub-units together.

The area for this is dimensional analysis and you can think of it like where each dimension is either a completely independent unit or can be considered as a function of other units: you use the same sort of ideas that you use in algebra to simplify units.

If you want to consider this kind of thing in mathematics, probably the best place to start is to look at the Cartesian product and how it is defined and visualized for various sets.

In fact what you are describing is not at all weird and the idea is used everywhere in mathematics when creating composite structures.

For example if you want to create a cylinder what you do is create something like T X R where T is a circle and R is a real line. You can also create a donut by using T X T.

This idea of creating new stuff like this is at the heart of modern mathematics when considering how to deal with very abstract ways of doing this kind of thing.

 

[thedy]

Hey thedy and welcome to the forums.

Typically a dimension in things like physics, engineering, and science (as opposed to mathematics) concerns the ratio of sets of units. In general you have a ratio of two units and those units are basically made up of multiplying other sub-units together.

The area for this is dimensional analysis and you can think of it like where each dimension is either a completely independent unit or can be considered as a function of other units: you use the same sort of ideas that you use in algebra to simplify units.

If you want to consider this kind of thing in mathematics, probably the best place to start is to look at the Cartesian product and how it is defined and visualized for various sets.

In fact what you are describing is not at all weird and the idea is used everywhere in mathematics when creating composite structures.

For example if you want to create a cylinder what you do is create something like T X R where T is a circle and R is a real line. You can also create a donut by using T X T.

This idea of creating new stuff like this is at the heart of modern mathematics when considering how to deal with very abstract ways of doing this kind of thing.

Hi,thanks for answer,I think,I found what I was looking for in your answer