Use ‘triangular numbers’ in a sentence | ‘triangular numbers’ example sentences
1- Gauss proved that every integer is the sum of at most 3 triangular numbers .
2- Moving inwards, the next pair of diagonals contain the triangular numbers in order.
3- The column formed by the set of rightmost rooms will correspond to the triangular numbers .
4- We take our lead from the geometrical considerations which attend G : the sum of the first seven, and the sum of the eight, were intended (most appropriately, in view of the triangular pedigree of the parameters!) to yield triangular numbers .
5- In a simple but remarkable instance of numerical geometry we find 10-as-triangle (known to the Pythagoreans as tetraktys) occupying a central position in a triangular setting of the perfect numbers, 6 and 28 (3rd and 7th triangular numbers , respectively).
6- The simplest of these arises directly from the operation of counting by reciting the sequence of natural numbers thus: “One, one plus two, one plus two plus three,…”, so generating the triangular numbers , 1, 3, 6, and so on, without limit.
7- Eventually, the term came to denote any number which, when added to a figurate number, generates the next higher number of the same shape ( triangular numbers , square numbers, pentagonal numbers, and so on).
8- The infinite sequence of triangular numbers diverges to +âˆ, so by definition, the infinite series 1 + 2 + 3 + 4 + ⋯ also diverges to +âˆ.
9- This equation was known to the Pythagoreans as early as the sixth century B.C.E. Numbers of this form are called triangular numbers , because they can be arranged in a triangle.
10- Gauss also discovered that every positive integer is representable as a sum of at most three triangular numbers on 10 July and then jotted down in his diary the note: “ΕΥΡΗΚΑ! num = Δ + Δ + Δ”.
11- For example, taking “m” to be 1 gives the triangular numbers 0, 1, 3, 6, … .
12- Elementary Evaluation of Certain Convolution Sums Involving Divisor Functions Elementary (i.e. not relying on the theory of modular forms) proofs of divisor sum convolutions, formulas for the number of ways of representing a number as a sum of triangular numbers , and related results.
More Sentences:
Related Words:
upper triangular matrix – triangular tile – truncated triangular – triangular mesh – triangular truss – triangular bandage – triangular slices – triangular numbers – triangular number – triangular prism – triangular matrix – triangular pyramid – triangular distribution – triangular design – triangular division –
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