Distribute small number of points on a disc Firstly I strongly know how many similar questions there are here.
It's about sets of evenly distributed points inside a circle.
If we need a big set of such points, good solutions are:


*

*Isocell method; Geogebra example

*Spirales method; Geogebra example
But it's interesting for me: 
if we have small number of points: 2,3,7,..
what is "the most" even configuration
and what is the optimization criterion to find it?
It seems that such configuration

is good for two points. But what about 5 points:

First or second?
I've been testing different optimizations: by area, by sum and variance of distances,
using Voronoi diagram etc. 
but not advanced further intuitive considerations.
 A: So we have set of several points $Set$ and some net $Net$, $Size[Net] \gg Size[Set]$
 covered unit disc.
On the greate advice of M. Wind  let's calculate value (GeoGebra code, intuitive clear):
s = Mean[
        Zip[
              Distance[p, ClosestPoint[Set, p]]
        , p, Net]
        ]

and try to minimize it, changing configuration of $Set$.
I've done many experiments with GeoGebra applets. First conclusion is:
All the results are independent from kind of $Net$ (isocell, spiral, random etc.)
if $Size[Net]$ is big enough.
First question is:
Is there another interesting and non-trivial optimization value?
I've tried 
s = Mean[
        Zip[
              Mean[
                       Zip[
                            Distance[p, ps]
                       ,ps,Set]
        , p, Net]
        ]

and some others. Method of M. Wind for now is the only effective and meanfull.
So came the turn of Wolfram Mathematica. After many intuitive attempts 
next results were obtained:


*

*Using "brutal force" of Mathematica optimization utilites (NMinimize[], e.g. Method -> {"NelderMead", "ShrinkRatio" -> 0.99,  "ContractRatio" -> 0.99, "ReflectRatio" -> 2})
one can get first approximations of distributes several points on a disc:





*I propose the hypothesis that 
any optimal configuration consists of several regular polygons, rotated relative to one another.
And we may optimize not points of $Set$, but radii and angles of rotation that is much faster and better.
Here is good example. Let $Size[Set]$=32. Here are four kind of sets:


*

*Spiral 32-net; s = 0.12649

*Isocell 32-net; s = 0.122737

*Direct optimization of configuration of 32 points on disc; s = 0.121151

*Smart optimization with manual selection of regular 
 polygons and numbers of vertices;
s = 0.120646

So I think the last attempt is a real method of the most uniform and symetrical distribution any number of points on a disc.
