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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: What about normalized gaps?
Date: Tue, 10 Sep 2024 14:11:56 -0700
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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.