# SD-WAN View Only
last person joined: 2 days ago

Forum to discuss Silver Peak EdgeConnect SD-WAN and Aruba SD- Branch. This includes SD-WAN Orchestration WAN edge network functions including routing, security, zone-based firewall, segmentation and WAN optimization, micro-branch solutions, best practices, third party integrations, All things SD-WAN!

## The radius of image of a circle under mobius transformation

This thread has been viewed 1 times
• #### 1.  The radius of image of a circle under mobius transformation

Posted Aug 11, 2021 08:04 AM

A Mobius transformation of the plane takes zaz+bcz+dz↦az+bcz+d. These are known to take circles to circles, but given an explicit circle, how do we compute the radius.

Let's parameterize our circle by z(t)=z0+re2πintz(t)=z0+re2πint. What is the radius and center of the image circle?

az(t)+bcz(t)+daz(t)+bcz(t)+d

I am looking for a computational proof that the image is a circle so I can find the (Euclidean) radius and centerIn my application, I have an approximate circle {z0+e2πint:t1NZ}{z0+e2πint:t∈1NZ} where NN is a large number. If we act the Mobius transformation pointwise, these spaces will no longer be evenly spaced out. So I decided it's better to compute the Euclidean center and radius if possible.

• #### 2.  RE: The radius of image of a circle under mobius transformation

Posted Aug 11, 2021 08:07 AM

Hello @ObviousKiwi !

It's really fascinating what you are doing, but how is it related to the HPE Networking?