Get-LatticePoints

I am so close to reaching the second level in Project Euler (need 50, I am at 48). Most of the problems that I have solved have been via Python, however, I am occasionally able to use PowerShell. A few of the problems ask to find lattice points within a circle.

What is a lattice point? - Think of a lattice point as an intersection on a grid. So if you had a circle with radius 1, there would be 5 lattice points: (-1,0), (0,1), (0,-1), (1,0) and (0,0).
Following is a PowerShell function that will get the number of lattice points for a given radius:

function Get-LatticePoints ([int]$radius)       
{       
    $count = 0       
    $x = -$radius       
    while ($x -le $radius)       
    {       
        $y = -$radius       
        While ($y -le $radius)        
        {       
            if($x*$x + $y*$y -le $radius*$radius)       
            {       
                $count++       
            }       
            $y++       
        }       
        $x++       
    }       
    return $count       
}       
       
for($i=1;$i -le 100;$i+=1) {       
   "Index: {0}`tLatticePoints: {1}" -f $i, (Get-LatticePoints $i)       
}

I forsee using this function in a couple of the Euler problems.

Enjoy!