# Does mobius transformation assume 3-D Euclidean space?

• I
• Layman FJ
In summary, the use of Möbius transformations in Newtonian physics is not applicable as they are purely mathematical operations. Similarly, considering rectilinear motion as circular motion along an infinite radius has no impact on the laws of physics.
Layman FJ
Are the assumptions in mobius transformation valid in Newtonian physics?

Möbius transformations are mathematical operations, they cannot be "valid in Newtonian physics". That's like asking "is the number 6 valid in Newtonian physics?"

mfb said:
Möbius transformations are mathematical operations, they cannot be "valid in Newtonian physics". That's like asking "is the number 6 valid in Newtonian physics?"
If we consider rectilinear motion as circular motion along a circle of infinite radius,will it be mathematically correct ?

You can do that, it has no relevance to physics how you call things.

mfb said:
You can do that, it has no relevance to physics how you call things.

## 1. What is a Mobius transformation?

A Mobius transformation is a mathematical function that maps points from one complex plane to another. It can also be thought of as a transformation of the entire complex plane.

## 2. Does a Mobius transformation assume 3-D Euclidean space?

Yes, a Mobius transformation assumes 3-D Euclidean space. It is a transformation that is defined in three-dimensional space and is often used to map points on a sphere onto a plane, which is a 3-D Euclidean space.

## 3. Can a Mobius transformation be applied to other types of spaces?

Yes, a Mobius transformation can be applied to other types of spaces, such as hyperbolic spaces and Riemann surfaces. However, the most commonly used space for Mobius transformations is 3-D Euclidean space.

## 4. Are there any real-world applications of Mobius transformations?

Yes, there are many real-world applications of Mobius transformations, particularly in physics, engineering, and computer graphics. They can be used to model and analyze complex systems, such as fluid dynamics and electromagnetic fields.

## 5. Is there a formula for calculating a Mobius transformation?

Yes, there is a general formula for calculating a Mobius transformation, which involves four complex parameters. This formula can be used to transform any point in 3-D Euclidean space to another point on the same plane.

• Differential Geometry
Replies
44
Views
1K
• General Math
Replies
1
Views
980
• General Math
Replies
29
Views
2K
• Quantum Physics
Replies
1
Views
1K
• General Math
Replies
11
Views
1K
• General Math
Replies
3
Views
1K
• Special and General Relativity
Replies
11
Views
562
• Differential Geometry
Replies
4
Views
2K
• General Math
Replies
2
Views
1K
• General Math
Replies
1
Views
1K