To detect patterns in the transcendental number pi, we can use the following formula : r{Ξ, Π, Ρ, Σ}{Θ,Λ,Μ,Ν}∞, ∞ ⊃ -1+⍵kxb.b2{κ,Θ,Λ,Μ,Ν}∞ {ω,Ξ,Π,Ρ,Σ}∞ &&μ{g} ,f,g,h,i,j⃝⇈<Ω ⍺ a,b,c,d,e⃝⇈ σ[{υ, φ, χ, ψ}, {ω, Ξ, Π, Ρ, Σ}∞]∞ This formula uses the notion of subsets, the Greek letters Ξ, Π, Ρ, Σ and Θ, Λ, Μ, Ν to calculate the sum of the transcendental number pi over an infinite range of values . The formula also uses addi- tional Greek letters such as ω and Ω to calculate the difference between the sum of the transcendental number and a constant . Additionally, the formula uses subscripts and superscripts to denote the specific range of values being considered in the calculation. Finally, the formula also uses the notation of b.b2 - 1 to...
The study presents some of the patterns observed in Pascal\u27s triangle in relation to combinatoric...
Abstract. LetSn be the symmetric group of permutations pi = pi1pi2 · · ·pin of {1, 2,..., n}. An in...
Pascal’s triangle is one of the most famous and interesting patterns in mathematics. In fact, while ...
This paper presents a catalogue of mathematical formulas and iterative algorithms for evaluating the...
Given two permutations σ ∈ Sk and pi = pi1... pin ∈ Sn, the permutation pi is said to contain the pa...
n≥0Sn. For pi, σ ∈ S, we say that σ contains pi if there is a subsequence of σ having the same relat...
In this paper we give rules for creating a number triangle T in a manner analogous to that for produ...
Integer compositions are ordered sequences of positive integers that sum up to a given integer. We u...
Given two permutations sigma (of length k) and pi (of length n), the permutation pi is said to conta...
Abstract. For pi ∈ Sn, let d(pi) be the arithmetic average of {|i − pi(i)|; 1 ≤ i ≤ n}. Then 0 ≤ d(p...
AbstractLet n,k be positive integers, with k⩽n, and let τ be a fixed permutation of {1,…,k}.11We wil...
In this study, a number pattern similar to Pascal\u27s triangle is presented. This number pattern re...
The 'Bailey-Borwein-Plouffe' (BBP) algorithm for {pi} is based on the BBP formula for {pi}, which wa...
We know that there is a variety of patterns in triangles in number theory. The Gilbreath's tri...
Includes bibliographical references.After discovering that a pattern existed in the sums of the digi...
The study presents some of the patterns observed in Pascal\u27s triangle in relation to combinatoric...
Abstract. LetSn be the symmetric group of permutations pi = pi1pi2 · · ·pin of {1, 2,..., n}. An in...
Pascal’s triangle is one of the most famous and interesting patterns in mathematics. In fact, while ...
This paper presents a catalogue of mathematical formulas and iterative algorithms for evaluating the...
Given two permutations σ ∈ Sk and pi = pi1... pin ∈ Sn, the permutation pi is said to contain the pa...
n≥0Sn. For pi, σ ∈ S, we say that σ contains pi if there is a subsequence of σ having the same relat...
In this paper we give rules for creating a number triangle T in a manner analogous to that for produ...
Integer compositions are ordered sequences of positive integers that sum up to a given integer. We u...
Given two permutations sigma (of length k) and pi (of length n), the permutation pi is said to conta...
Abstract. For pi ∈ Sn, let d(pi) be the arithmetic average of {|i − pi(i)|; 1 ≤ i ≤ n}. Then 0 ≤ d(p...
AbstractLet n,k be positive integers, with k⩽n, and let τ be a fixed permutation of {1,…,k}.11We wil...
In this study, a number pattern similar to Pascal\u27s triangle is presented. This number pattern re...
The 'Bailey-Borwein-Plouffe' (BBP) algorithm for {pi} is based on the BBP formula for {pi}, which wa...
We know that there is a variety of patterns in triangles in number theory. The Gilbreath's tri...
Includes bibliographical references.After discovering that a pattern existed in the sums of the digi...
The study presents some of the patterns observed in Pascal\u27s triangle in relation to combinatoric...
Abstract. LetSn be the symmetric group of permutations pi = pi1pi2 · · ·pin of {1, 2,..., n}. An in...
Pascal’s triangle is one of the most famous and interesting patterns in mathematics. In fact, while ...