This is what I came up with. Here is a fiddle.
First, I need three wrapper elements for both a square shape and centered text.
<div><div><div>Lorem ipsum dolor sit amet, consectetuer adipiscing elit,
sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat
volutpat.</div></div></div>
This is the stylecheet. It makes use of two techniques, one for square shapes and one for centered text.
body > div {
position:relative;
height:0;
width:50%; padding-bottom:50%;
}
body > div > div {
position:absolute; top:0;
height:100%; width:100%;
display:table;
border:1px solid #000;
margin:1em;
}
body > div > div > div{
display:table-cell;
vertical-align:middle; text-align:center;
padding:1em;
}