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    Triangular number - Wikipedia

    https://en.wikipedia.org/wiki/Triangular_number

    A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The nth triangular number is the number of dots in the triangular arrangement with n dots on each

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    The triangular numbers are given by the following explicit formulas:
    The first equation can be illustrated using a visual proof. For every triangular number , imagine a "half-square" arrangement of objects corresponding to

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    Triangular numbers have a wide variety of relations to other figurate numbers.
    Most simply, the sum of two consecutive triangular numbers is a

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    Triangular numbers correspond to the first-degree case of Faulhaber's formula.
    Alternating triangular numbers (1, 6, 15, 28, ...) are also hexagonal

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    A fully connected networkof n computing devices requires the presence of Tn − 1 cables or other connections; this is equivalent to the

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    An alternative name proposed by Donald Knuth, by analogy to factorials, is "termial", with the notation n? for the nth triangular number. However, although some other sources use this name and notation, they are not in wide use.

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    1 + 2 + 3 + 4 + ⋯
    Doubly triangular number, a triangular number whose position in the sequence of triangular numbers is also a

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    By analogy with the square root of x, one can define the (positive) triangular root of x as the number n such that Tn = x:
    which follows immediately from the quadratic formula.

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  2. Triangular number - Simple English Wikipedia, the free ...

    https://simple.wikipedia.org/wiki/Triangular_number

    A triangular number is a number that is the sum of all of the natural numbers up to a certain number. When formed using regularly spaced dots, they tend to form a shape of equilateral triangle, hence the name.

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    • Doubly triangular number - Wikipedia

      https://en.wikipedia.org/wiki/Doubly_triangular_number

      In mathematics, the doubly triangular numbers are the numbers that appear within the sequence of triangular numbers, in positions that are also triangular numbers. That is, if denotes the th triangular number, then the doubly triangular numbers are the numbers of the form .

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    • Triangular number - Wikipedia

      https://en.wikidark.org/wiki/Triangular_number

      21/07/2021 · A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n.

    • Número triangular – Wikipédia, a enciclopédia livre

      https://pt.wikipedia.org/wiki/Número_triangular
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      Em geral, o n-ésimo número triangular é dado por:T n = ∑ k = 1 n k = 1 + 2 + 3 + ⋯ + ( n − 2 ) + ( n − 1 ) + n = n ( n + 1 ) 2 = ( n + 1 2 ) {\displaystyle T_{n}=\sum _{k=1}^{n}k=1+2+3+\dotsb +(n-2)+(n-1)+n={\frac {n(n+1)}{2}}={n+1 \choose 2}} A primeira equação pode ser demonstrada por uma prova visual.[1] Para cada núm…
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      • Category:Triangular numbers - Wikimedia Commons

        https://commons.wikimedia.org/wiki/Category:Triangular_numbers

        Media in category "Triangular numbers". The following 59 files are in this category, out of 59 total. 153 Triangular.gif 1,576 × 1,688; 101 KB. 3eckszahl rechteck.PNG 70 × 60; 351 bytes. 3eckszahl treppe2.PNG 33 × 60; 226 bytes. 3eckszahl treppe3.PNG 42 × 60; 244 bytes. 3eckszahl treppe4.PNG 51 × 60; 287 bytes.

      • Triangular number | Math Wiki | Fandom

        https://math.fandom.com/wiki/Triangular_number
        • A triangular number is the number of dots in an equilateral triangle evenly filled with dots. For example, three dots can be arranged in a triangle; thus three is a triangle number. The -th triangle number is the number of dots in a triangle with dots on a side. A triangle number is, equivalently, the sum of the natural numbers from 1 to. As shown in the rightmost term of this formula, every …
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      • Triangular numbers - OeisWiki

        https://oeis.org/wiki/Triangular_numbers

        20/01/2013 · The th triangular number is thus one half of the th pronic number (or oblong number). A000217 Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n, n ≥ 0. {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, , 561, 595, 630, 666, 703, 741, 780, ...}

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