Reiman sphere mobius transforms and inverse square

In summary, a Reiman sphere is a mathematical construct used to represent complex numbers in three-dimensional space, named after mathematician Hans Reiman. A Mobius transform is a type of complex function that maps points from the complex plane onto itself, represented by the formula f(z) = (az + b) / (cz + d). The Reiman sphere can be used to visualize and understand Mobius transforms, with each point on the sphere corresponding to a unique Mobius transform. An inverse square function is a mathematical function that has the form f(x) = a/x^2, commonly used in describing the relationship between two variables that decrease or increase at a rate proportional to the square of the distance between them. Reiman sphere and Mob
  • #1
zwoodrow
34
0
has anyone ever seen analysis of inverse square problems using the points in the plane mapped onto the reiman sphere.
 
Mathematics news on Phys.org
  • #2
His name was Riemann, not reiman.
 

1. What is a Reiman sphere?

A Reiman sphere is a mathematical construct that is used to represent the complex numbers in three-dimensional space. It is named after the mathematician Hans Reiman.

2. What is a Mobius transform?

A Mobius transform, also known as a Mobius transformation, is a type of complex function that maps points from the complex plane onto itself. It is represented by the formula f(z) = (az + b) / (cz + d), where a, b, c, and d are complex numbers and z is the input value.

3. What is the relationship between Reiman sphere and Mobius transforms?

The Reiman sphere can be used to visualize and understand Mobius transforms. Each point on the Reiman sphere corresponds to a unique Mobius transform, and the transformation of points on the sphere can be interpreted as the transformation of complex numbers by the Mobius function.

4. What is an inverse square function?

An inverse square function is a mathematical function that has the form f(x) = a/x^2, where a is a constant and x is the input value. It is commonly used to describe the relationship between two variables that decrease or increase at a rate proportional to the square of the distance between them.

5. How are Reiman sphere, Mobius transforms, and inverse square functions related?

Reiman sphere and Mobius transforms are often used in the study of inverse square functions, particularly in complex analysis. The Reiman sphere allows for a visual representation of the complex numbers, which are essential in understanding Mobius transforms. Inverse square functions can also be represented using Mobius transforms, providing a useful tool for analyzing their properties.

Similar threads

Replies
2
Views
981
Replies
3
Views
659
  • Introductory Physics Homework Help
Replies
8
Views
856
  • Mechanics
Replies
5
Views
1K
  • General Math
Replies
7
Views
1K
Replies
6
Views
911
Replies
12
Views
260
Replies
2
Views
1K
  • General Math
Replies
2
Views
1K
Back
Top