Triangular numbers

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Related to Triangular numbers: Square numbers, Pentagonal numbers
(Math.) the series of numbers formed by the successive sums of the terms of an arithmetical progression, of which the first term and the common difference are 1. See Figurate numbers, under Figurate.

See also: Triangular

Webster's Revised Unabridged Dictionary, published 1913 by G. & C. Merriam Co.
References in periodicals archive ?
His topics include dragons and poison, averages via distances, inner triangles, land or water, flipping a coin for a year, Gauss' shoelace formula, subdividing a square into triangles, broken sticks and Viviani's theorem, one more question about integer right triangles, counting triangular and square numbers, very triangular and very very triangular numbers, and compositional square roots.
Now the derived points are the triangular numbers starting with zero, and therefore the general formula for D is:
Triangular numbers have been studied since the ancient Greeks.
The three lessons are based on investigations into triangular numbers, providing an alternative to the linear functions work we generally see in this area.
The next section provides a brief discussion on the concept of superiority and inferiority for fuzzy triangular numbers. In Section 3, the problem is presented and Section 4 discusses the solution methods.
In this method according to the number of options the membership function is considered as the following illustration and triangular numbers are also determined in this way.
Therefore, Xu [22] proposed a dynamic geometric aggregation operator, which applies three representation formats, say, real number, interval number, and triangular number (triangular numbers are used to transform linguistic labels), for dynamic hybrid multiattribute group decision making (DHMADM).
In this paper we used a new aspect of fuzzy time function which represents a combination of time and fuzzy triangular numbers.
The squares make up the perfect pangram I'D PAY, but despite a good consonant-vowel balance it is difficult to get anything out of the triangular numbers, for which the relevant letters are ACFJOU.
Similarly to right and left triangular numbers we can introduce right and left trapezoidal numbers as parts of a trapezoidal number.
A mate went for the same effect, but his odd triangular numbers looked like bushy wedges of Dairylea.
Well done to Dominic Degnan from County Durham who correctly worked out that 1, 3, 6, 10, 15, 21 are triangular numbers in last fortnight's quiz.