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I noticed when trying to make a string of 6 circ symbols that the last one is closer to the one beside it than the rest of them, after playing with it for a while it looks like an even number (greater than 2) of circ causes this, how can I fix the spacing so it is even?

Example:

documentclass{article}

begin{document}

1 circ: $circ  $



2 circ: $circ circ $



3 circ: $circ circ circ$



4 circ: $circ circ circ circ$



5 circ: $circ circ circ circ circ $



6 circ: $circ circ circ circ circ circ $



7 circ: $circ circ circ circ circ circ circ $



end{document}

From the TeXbook (page 187, solution on page 326)

Exercise 19.7

B. L. User tried typing ‘eqno(*)’ and ‘eqno(**)’,
and he was pleased to discover that this produced the equation numbers
‘(∗)’ and ‘(∗∗)’. [He had been a bit worried that they would come out
‘(*)’ and ‘(**)’ instead.] But then a few months later he tried
‘eqno(***)’ and got a surprise. What was it?

When you type an asterisk in math mode, plain TeX considers
* to be a binary operation. In the cases ‘(*)’ and ‘(**)’, the
binary operations are converted to type Ord, because they don't appear in
a binary context; but the middle asterisk in ‘(***)’ remains of type Bin.
So the result was ‘(∗ ∗ ∗)’. To avoid the extra medium spaces, you can
type ‘eqno(*{*}*)’; or you can change mathcode`*, if you never use
* as a binary operation.

It doesn't matter if we're in an equation number (eqno); the main issue is math mode where the behavior shows. Since circ is a binary operation symbol just like *, you get the same.

If you want evenly spaced circ symbols you can use

{circ};{circ};{circ};{circ}

Even better, define a suitable command:

documentclass{article}

usepackage{xparse}



ExplSyntaxOn

NewDocumentCommand{circs}{m}

 {

  ensuremath

   {{

     {circ}prg_replicate:nn { #1 - 1 } { ; {circ} }

   }}

 }

ExplSyntaxOff



begin{document}



$circs{1}$



$circs{2}$



$circs{3}$



$circs{4}$



$circs{5}$



$circs{6}$



$circs{7}$



end{document}

When you issue showcirc you'll see it defined as mathchar"220E. The first number in this definition points to the intrinsic "format" of the character. 2 denotes a binary operator which has a specific spacing around. So, circ is considered a binary operator and therefore expects operands on either side. Odd-numbered circs show better alignment as they supply "operands" on either side (barring accommodation for uniform spacing around consecutive circs):

documentclass{article}



begin{document}



1 circ: $circ$



2 circ: $circ circ$



2 circ: $circ circ {}$



3 circ: $circ circ circ$



4 circ: $circ circ circ circ$



4 circ: $circ circ circ circ {}$



5 circ: $circ circ circ circ circ $



6 circ: $circ circ circ circ circ circ$



6 circ: $circ circ circ circ circ circ {}$



7 circ: $circ circ circ circ circ circ circ$



end{document}

If you just want to list a number of circs with the correct spacing, consider adding a empty math group at the end when using an even number of circs. Alternatively, use {circ} or mathord{circ} to avoid the surrounding space; mathord turns its argument into a math ordinal.