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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 each side, and is equal to the sum of the n natural ...
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean polygonal number; a number represented as a discrete r-dimensional regular geometric pattern of r ...
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 T n = n ( n + 1 ) / 2 {\displaystyle T_{n}=n(n+1)/2} denotes the n {\displaystyle n} th triangular number, then the doubly triangular numbers are the numbers of the form ...
The first six triangular numbers. The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula
In mathematics, a polygonal number is a number that counts dots ... 66 91 120 153 190 2 ln 2 [3 ... A computer search for pentagonal square triangular numbers has ...
Is the sum of all the numbers on a roulette wheel (0 through 36). [19] This is a corollary of the fact that the number is a Triangular number, as mentioned earlier. Was a winning lottery number in the 1980 Pennsylvania Lottery scandal, in which equipment was tampered to favor a 4 or 6 as each of the three individual random digits. [21]
Layers of Pascal's pyramid derived from coefficients in an upside-down ternary plot of the terms in the expansions of the powers of a trinomial – the number of terms is clearly a triangular number. In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by
Each centered triangular number has a remainder of 1 when divided by 3, and the quotient (if positive) is the previous regular triangular number. Each centered triangular number from 10 onwards is the sum of three consecutive regular triangular numbers. For n > 2, the sum of the first n centered triangular numbers is the magic constant for an n ...