Figurative references to circles, squares, and triangles turn up in a variety of familiar expressions. Here’s a list of many of those idioms and their meanings.
1. To be a square peg in a round hole is to be someone who doesn’t fit in a particular environment, or in certain circumstances.
2. To go back to square one is to start over again because of a setback or an impasse.
3. The expression “Be there, or be square” alludes to often-lighthearted pressure to attend an event or suffer the consequences of being considered conventional and uninteresting.
4–6. To call something square, square something with someone, or square accounts is to agree with another party that neither party owes anything to the other one.
7. To circle around is to move in a circular motion to engage in reconnaissance or to figuratively evaluate a situation.
8. A circular argument is one in which the proposition is assumed to be true.
9. To come (or go) full circle is to figuratively return to one’s starting point.
10. Someone who could fight a circle saw is so tough that the thought of sparring with a deadly power tool does not faze him or her.
11. To say that something doesn’t cut any squares with one means that one refuses to be influenced.
12. To be fair and square is to treat everyone impartially.
13. To look someone square in the eye is to do so directly, indicating honesty.
14. A love, or eternal, triangle is a circumstance in which two people are in love with the same person.
15. To move in the same circles with someone is to have similar tastes and frequent the same locations.
16. Something on the square is done fairly, honestly, and openly.
17. To be out of square is to not be in agreement.
18. To run circles around (or run rings around) someone is to figuratively outcompete him or her to the extent that the other person seems to be standing still.
19. To run around in circles is to figuratively expend much effort with little result because of poor organization or planning.
20. A square answer is an honest one.
21. To square away is to rectify or put in order.
22. A square deal is a fair deal.
23. A square meal is a complete, nutritious set of food servings. “Three square meals” (often abbreviated to “three squares”) refers to the traditional daily schedule of breakfast, lunch, and dinner (or supper).
24. To square off is to prepare to fight or compete.
25. To square up is to settle or reconcile. It also means to confront someone or something courageously.
26. To square one’s shoulders is to literally straighten one’s shoulders before undertaking a difficult task or to figuratively prepare oneself for an effort.
27. To attempt to square the circle is to try to do the impossible.
28. To square something with someone means to obtain approval or permission
29. To speak or talk in circles is to discuss an issue or problem repetitively with no progress.
30. A vicious circle (or vicious cycle) is one in which solutions create new problems.