Closed Form for Triangular Numbers/Historical Note
Jump to navigation
Jump to search
Historical Note on Closed Form for Triangular Numbers
Some sources report that the closed-form expression for the $n$th triangular number was proved by Archimedes during the course of his proofs of the volumes of various solids of revolution in his On Conoids and Spheroids.
Others suggest that it was known as far back as Pythagoras of Samos, circa $550$ B.C.E.
Sources
- 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $1$: Some Preliminary Considerations: $1.3$ Early Number Theory: Problems $1.3$: $1 \ \text {(a)}$
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.5$: Archimedes (ca. $\text {287}$ – $\text {212}$ B.C.)