Work out triangular number instantly with clear inputs, formula shown and shareable results.
The nth triangular number counts dots in a triangular array and equals n(n + 1)/2. A value v is triangular exactly when 8v + 1 is a perfect square.
Triangular number
Tₙ = n(n + 1) / 2
Triangular test
v is triangular ⇔ 8v + 1 is a perfect square
20 × 21 / 2 = 210, which is also the number of handshakes among 21 people.
1, 36, 1225, 41616 and so on — an infinite family generated by the Pell equation.