Explanation of slerp example in reference

Hey, the Vector3 slerp example in the Script reference contains the following. I've commented what I understand from it and reading wikipedia on slerp.

 using UnityEngine;
 using System.Collections;
 
 public class example : MonoBehaviour {
   public Transform sunrise;
   public Transform sunset;
 
   void Update() {
       // Is this first line a typo? When I tried this I divided the sum of
       // both positions instead of doing what they do here and it seemed
       // to work like it was supposed to. E.g. the object arced y-axis. In
       // contrast, using the code here caused it to arc on the z-axis. Anyway
       // this should be the midpoint between both positions.
       Vector3 center = sunrise.position + sunset.position * 0.5F;

       // Offset the midpoint so we now have the center of our arc. However, it's
       // offset in the negative y direction, whereas you'd think it would be offset
       // in the positive y direction.
       center -= new Vector3(0, 1, 0);

       // Sunrise position relative to the center, so this will be in the positive
       // y direction.
       Vector3 riseRelCenter = sunrise.position - center;

       // Sunset position relative to the center, in +y direction.
       Vector3 setRelCenter = sunset.position - center;

       // Magic. Reference says 'interpolates from toward to by amount t'. The t
       // argument isn't confusing, I get that they are just taking advantage of
       // using the decimal values during the first second. But what are the first
       // two parameters supposed to be exactly? Are they supposed to be start and
       // end positions relative to our center? Again though, why is the center
       // located below where the actual center of the arc is (at least from what
       // I saw by running the example).
       transform.position = Vector3.Slerp(riseRelCenter, setRelCenter, Time.time);

       // No idea.
       transform.position += center;
   }
 }

I tried the above just having a cube arc from one position from another, with the only change being the center being originally calculated as (sunrise.position + sunset.position) 0.5 rather than sunrise.position + (sunset.position 0.5) as above. The cube in the +y direction from one point to another. If I left the example was it was without changing the first statement it arced in the positive z direction.

Just looking for an explanation of what's going on. Particularly the reason for calculating center in that way, and adding center to the position at the end.