The fighting area for participants in a combat sport. Origianally, these sports took place in a circle. When support ropes were added to clearer identify the border, the rings were made sqaure or rectangular in shape.

See also ring, boxing ring, wrestling ring, enter the ring, queensbury
As these two competitors enter the sqaured circle, they begin to realise that for one of them, fame and fortune on a tremedous scale awaits after this bout.
by kung-fu jesus August 19, 2004
Based on the interpretation of the Libertarians Against Capitalism, this phrase would have to be considered a logical contradiction, like "square circle."
by AustroLibertarian-UD May 17, 2010
A U.S. Marine term for getting stuck on a Naval Ship that patrols one area for far too long of a time.

When a Naval ship gets sent to an area they are given a grid or "Square" that they are allowed to move around in or patrol. They do not leave this area unless assigned to move on. So when they get assigned to one grid for a very long time they are in essence just doing a bunch of circles patrolling that zone.

Hence the term: Squared Circles
"We got stuck doing squared circles in the Gulf for 3 months until we were finally able to hit a port!"
by purenrgy December 29, 2010
Describing a hopeless, meaningless, or vain undertaking.

Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.

In 1882, the task was proven to be impossible.
In Spanish, the expression "descubriste la cuadratura del círculo" or square the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle by using only a finite number of steps with compass and straightedge. More abstractly and more precisely, it may be taken to ask whether specified axioms of Euclidean geometry concerning the existence of lines and circles entail the existence of such a square.

In 1882, the task was proven to be impossible," ("you discovered the quadrature of the circle") is often used derisively to dismiss claims that someone has found a simple solution to a particularly hard or intractable problem.
by bbennet111 August 16, 2010
Nobody likes to hang around boring/dull persons for more than half a sec. Having no squares in your circle means your closest ones' group is interesting, driven and adventurous; you stand out as opposed to fitting in.
"… I wanna be somebody, somebody that's never been
No squares in my circle, best shape I ever been"
by rafreyes November 11, 2019