What is the Definition of Dimension in Mathematics?

AI Thread Summary
A dimension in mathematics is defined as the minimum number of coordinates needed to specify a point within a space, with N dimensions requiring N numbers in any coordinate system. The commonly referenced example is our four-dimensional space-time, which includes three spatial dimensions and one temporal dimension. Various definitions of dimension exist, such as Hausdorff and Lebesgue covering dimensions, each serving different mathematical contexts. Understanding these definitions is crucial for exploring complex mathematical concepts and theories. The concept of dimension is fundamental to both geometry and physics.
Dimitri655
Messages
11
Reaction score
0
Hey guys!

After watching another awesome video of minutephysics:


I couldn't help but wonder, what is a dimension?

Thanks for your replies in advance,
 
Physics news on Phys.org
I think dimension is most clearly defined mathematically, if a space need at least N numbers in anyone of its coordinate systems, then the space is of N dimension. The space-time we live in is 4 dimensional, which includes 3 number to denote location, and one number to denote time.
 
There are many different types of definitions of dimension in Mathematics: Hausdorff, Lebesgue covering, etc.
 

Thread 'The Physics of unloading sand from a barge'

I think it's easist first to watch a short vidio clip I find these videos very relaxing to watch .. I got to thinking is this being done in the most efficient way? The sand has to be suspended in the water to move it to the outlet ... The faster the water , the more turbulance and the sand stays suspended, so it seems to me the rule of thumb is the hose be aimed towards the outlet at all times .. Many times the workers hit the sand directly which will greatly reduce the water...
View full post »

Thread 'Why can't Solar panels be hemispherical, or a curved strip type?'

comparing a flat solar panel of area 2π r² and a hemisphere of the same area, the hemispherical solar panel would only occupy the area π r² of while the flat panel would occupy an entire 2π r² of land. wouldn't the hemispherical version have the same area of panel exposed to the sun, occupy less land space and can therefore increase the number of panels one land can have fitted? this would increase the power output proportionally as well. when I searched it up I wasn't satisfied with...
View full post »

Similar threads

B What Is the Fourth Dimension and How Does It Work?
Replies
3
Views
2K
B What Are the Dimensions of kWh?
Replies
3
Views
5K
B The Fourth Dimension: A Measurement of Aging
Replies
20
Views
3K
Technical drawing: reference dimensions
Replies
12
Views
3K
What are the dimensions/units of Evaporation?
Replies
12
Views
4K
A Correcting units from this physics paper?
Replies
1
Views
2K
B I can't understand more than 3 spatial dimensions
Replies
6
Views
3K
I Mass Dimension of Fields (Momentum space)
Replies
2
Views
1K
Understand Phase & Dimension: Self-Taught Guide
Replies
2
Views
2K
Is a Second Temporal Dimension Possible?
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top