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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -




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Topic review (newest first)

2013-04-21 18:40:40

Many thanks bobbym

I will search for those progs in out coder section.

2013-04-21 03:21:27


There are programs to do that. You could maybe find one and then it will take your points that are in (x,y,z) and render them on your screen. They also rotate, dilate, translate, generally anything you can imagine.

Here is an example with 500 random points on a sphere.

2013-04-21 03:02:58

A good 3-d plotter would give you a model of the dots - a model you could hold in your hands and twist about to see really what was where.
So what are the BEST ways of simulating "twist about to see really what was where" on a flat computer screen?.

2013-04-21 01:46:00


I am not sure I am following you. To show those points you will have to get a 3D plotting program.

2013-04-20 22:29:04

bobbym wrote:


You would need a 3D plotter.

Is there a good way to simulate a 3-d plotter on a computer screen?

2013-04-20 18:26:38


You would need a 3D plotter.

2013-04-20 17:15:08

The simplest idea so far is this:-
For N>2 points, each point has a neighbour that is nearer than of all the others.
Lets make this distance as great as we can without going outside the sphere.
VERY SMALL increments are best!

We now REPEAT this for every single point in turn.
Now each point ends up max-spaced from its nearest neighbour

This is ONE variety of evenly-spaced.
But is it the only one?

To SEE this we need a way to visualise the pattern of points (on a flat screen)
For example for N=5 there is one pattern (of several?)
When we add a point we now have N=6 points.
If we could SEE how the points moved when we added that point it would help us begin to understand "what is happening" and why!

PLease suggest some ideas of how to visualise points scattered on or inside a sphere.
Many thanks

2012-07-05 00:00:48


But for all other  N there are as many "best srrangements" as the number of ways we care to define "best even placement" - how many neighbours are at WHICH distance

That may be true, there are certainly numerous ways. You can pick one that you can solve, or is computationally feasible.

2012-07-04 23:51:01

So for N=2,3,4,6,8.12,20,30 there is ONE best pattern of dots for each N
But for all other  N there are as many "best srrangements" as the number of ways we care to define "best even placement" - how many neighbours are at WHICH distance.

2012-07-04 22:24:37

Hi Mrwhy;

In mathematics or any other problem solving field we rarely have the choice of picking what we want. Very often it is what we are capable of doing that decides what we can pick. Pick some very, very simple criterion and use that.

2012-07-04 22:13:35

Yes indeed - we must say what we decide we mean by "evenly spaced"

For the cases N=2,3,4,6,8,12,20,30 it is plain enough
We mean maximally spaced but in groiups as large as possible the distances to be equal

For example for N=8 we want every dot to be equal distance from every other of 3 other dots and equal spaced but more distant from three other dots.

For N=4,5,7,,9,10,11 etc we can make up similar rules

But for all N>4 we need to say what weight we give to the dots closest compared to those farther away. In that way we decide which dot-arrangement is best for each N in turn.

This is where I am stuck and need your ideas and suggestions

2012-07-04 04:26:15

To do better you would have to define the criterion of measure of space.

2012-07-04 02:17:09

I was trying "Quick Reply" and after it had already acknowledged I was signed on
Quick Reply is denioed with idiot message endinmg  "Say when"

I was trying to send you a reference illustrating the vast difference between random and uniform
Random means irregular!

The ref is now lost and I have spent an hour trying to recover it - sorry abiut that.

To DENY crystalline's claim to be more uniform we need a way to MEASURE uniformity of spacing

2012-07-04 02:01:00


I am not following you. Are you having trouble posting?

2012-07-04 01:56:22

testing why it refuses to allow me to reply

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