Re: What about normalized gaps?

On 9/10/2024 1:45 PM, Chris M. Thomasson wrote:

To normalize the distance between two points in n-ary space. p0 and p1 can be n-ary vectors.
 p0 = 1/2
p1 = 1/1
pdif = p1 - p0
 the mid point would use the unit fraction 1/2 at:
 pmid = p0 + pdif * 1/2
 right?
 For say a 3d vector of the above would be:
 p0 = (1/2, 0, 0)
p1 = (1/1, 0, 0)
 We can plot these. Say
  p0 = (1/2, 1/4, 1/1)
p1 = (1/2, 1/3, -1/8)
 That is a line in pure 3d space, yet the line normalization still works. The unit fraction 1/2 is half way in between p0 and p1...
 pdif = p1 - p0
pmid = p0 + pdif * 1/2
 Right?

Wrt normalizing it where p0 + pdif * 0 = p0 and p0 + pdif * 1 = p1 allows us to use unit fractions to find points on the line from p0 to p1? For instance p2 would be 1/4 across from p0 to p1 where:
p2 = p0 + pdif * 1/4
Draw a line from p0 to p2.