hey all,(adsbygoogle = window.adsbygoogle || []).push({});

I was wandering if there was a way to spread vectors as evenly as possible through space (all originating from the same point.

In 2D, this is easy, i just divide a unit circle into the number of peices i require (or in the specific case i'm looking at it for, i divide the 1^{st}quadrant into that many peices).

In 3D it gets harder though. i figured it's effectively the same thing as spreading dots evenly around a sphere, and it seems there's no way (on the internet) to do this other than via algorithms.

would it be possible to achieve what i'm looking for using Matrices?

i.e.

[tex]\begin{pmatrix}

a1\\

a2\\

a3

\end{pmatrix}

\begin{pmatrix}

b1\\

b2\\

b3

\end{pmatrix}

\begin{pmatrix}

c1\\

c2\\

c3

\end{pmatrix}

[/tex]

are my vectors i want to spread out as much as possible (all the same length).

if i take

[tex]

\begin{pmatrix}

a1&b1&c1\\

a2&b2&c2\\

a3&b3&c3

\end{pmatrix}

[/tex]

and it's transpose, and multiply them, i'll get a symetric matrix with 1s down the leading diagonal (dot product with itself) and numbers less than one (other dot products) everywhere else.

what i'm asking is if there's a way to minimise all the entries of this matrix so that the sum of them all is as small as possible? And would that result in having my vectors evenly spread out around the space?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Spreading vectors around an area

**Physics Forums | Science Articles, Homework Help, Discussion**