triangular number

noun

: a number (such as 3, 6, 10, 15) representable by that many dots arranged in rows that form a triangle and that equals n(n+1)2 for some positive integer value of n

Word History

First Known Use

1795, in the meaning defined above

Time Traveler
The first known use of triangular number was in 1795

Rhymes for triangular number

See All Rhymes for triangular number

Browse Nearby Words

triangular crab
triangular number
triangular numbers
See all Nearby Words

Cite this Entry

“Triangular number.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/triangular%20number. Accessed 1 Apr. 2025.

Copy Citation

Share

Kids Definition

triangular number

noun
: a power series that gives the expansion of a function f(x) in the neighborhood of a point a provided that in the neighborhood the function is continuous, all its derivatives exist, and the series converges to the function in which case the first term of the series is f(a) and the (n + 1)st term consists of the factor (x - a) raised to the exponent n and multiplied by a coefficient consisting of a fraction whose numerator is the derivative of nth order of f(x) evaluated at a and whose denominator is n!

More from Merriam-Webster on triangular number

Britannica.com: Encyclopedia article about triangular number

Love words? Need even more definitions?

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!

Popular in Grammar & Usage

See More

How to Use Em Dashes (—), En Dashes (–) , and Hyphens (-)

The Difference Between 'i.e.' and 'e.g.'

Why is '-ed' sometimes pronounced at the end of a word?

Words You Always Have to Look Up

Democracy or Republic: What's the difference?
See More

Popular in Wordplay

See More

What do SCOTUS, POTUS, and FLOTUS mean?

Top 10 Sophisticated Insults

More Words with Remarkable Origins

Terroir, Oenophile, & Magnum: Ten Words About Wine

8 Words for Lesser-Known Musical Instruments
See More

Popular

See More

How to Use Em Dashes (—), En Dashes (–) , and Hyphens (-)

What do SCOTUS, POTUS, and FLOTUS mean?

Top 10 Sophisticated Insults
See More

Games & Quizzes

See All
Play Quordle: Guess all four words in a limited number of tries. Each of your guesses must be a real 5-letter word.
Quordle Can you solve 4 words at once?
Play Blossom: Solve today's spelling word game by finding as many words as you can using just 7 letters. Longer words score more points.
Blossom Word Game Pick the best words!
Play Missing Letter: a crossword with a twist. Each of the 25 puzzle words start with a different letter of the alphabet. Which letter is missing?
Missing Letter A daily crossword with a twist
burrowing owl athene cunicularia tilts its head outside its burrow on marco island florida
Guess the Curious Origins of These Everyday Words Oh, that’s where that comes from…
See All