A particular way of organising a proof using two parallel columns is often used in elementary geometry classes in the United States. The proof is written as a series of lines in two columns. In each line, the left-hand column contains a proposition, while the right-hand column contains a brief explanation of how the corresponding proposition in the left-hand column is either an axiom, a hypothesis, or can be logically derived from previous propositions. The left-hand column is typically headed "Statements" and the right-hand column is typically headed "Reasons".

বৈপরিত্য দ্বারা প্রমাণ
Heuristic mathematics and experimental mathematics
Two-column proof
Computer-assisted proofs