How this calculation works
The index tells how many rows a triangular dot pattern has when row sizes run from 1 up to that index.
THE FORMULA
n is triangular when 8n + 1 is an odd perfect squareA worked example
55 = 1 + 2 + … + 10.
Good to know
Zero is treated as the zeroth triangular number.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Check whether the input is a sum of the first k positive integers.
The primary result is labeled “Triangular?”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Zero is treated as the zeroth triangular number.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
55 = 1 + 2 + … + 10.
Which rule does this calculator apply?
n is triangular when 8n + 1 is an odd perfect square