This study aims at knowing and describing students' mathematical communication skills in problem-solving on Pythagorean theorem material based Polya's procedure. The phase consists of the stage understanding problems, planning problem solving, implementing plans, re-examining. subject this were 6 students from eighth-grade Junior High School which was selected good, sufficient, poor criteria. M...

A pair ( a , b ) of positive integers is pythagorean if 2 + = □ i.e. square). called double-pythapotent there another k l such that pair, and it quadratic pythapotent which not multiple pair. To each we assign an elliptic curve Γ with torsion group Z / × 4 has rank over Q only Similarly, to 8 Moreover, in the later case obtain every isomorphic form where As side-result get then are infinitely m...

Nature displays profound preference for certain specific ratios to design her life-forms. These are geometric relationships that are transcendent and originated from Sacred Geometry. The view that geometry had a ritual origin is a part of a wider view that civilisation itself had a ritual origin, and therefore the history of utilisation of Sacred Geometry by man goes back to many centuries ago....

Abstract This article presents the circular Pythagorean fuzzy set (C-PFS) model, a generalization of intuitionistic model that improves its performance thanks to acclaimed extension sets sets. Then, we generalize C-PFSs produce novel disc (D-PFSs). The constituent elements both and D-PFSs are values, either with common or distinctive radius. We lay out some fundamental algebraic arithmetic oper...

Abstract The similarity measures are essential concepts to discuss the closeness between sets. Fuzzy and intuitionistic fuzzy dealt with incomplete inconsistent data more efficiently. With time in decision-making theory, a complex frame of environment that occurs cannot be specified entirely by these A generalization like Pythagorean set can handle such situation applicability this attracted re...

For n ∈ N consider the n-dimensional hypercube as equal to the vector space F2 , where F2 is the field of size two. Endow F2 with the Hamming metric, i.e., with the metric induced by the `1 norm when one identifies F2 with {0, 1} ⊆ R. Denote by `2 (F2 ) the n-fold Pythagorean product of F2 , i.e., the space of all x = (x1, . . . , xn) ∈ ∏n j=1 F n 2 , equipped with the metric ∀x, y ∈ n ∏ j=1 F2...

In his recent paper[l], Sastry defines two triangles T(a,b,c) and T(a',b',c') to be Smarandache related ifS(a) = Sea'), S(b) = S(b') and S(c) = S(c'). The function S is known as the Smarandache function and is defmed in the following way. For n any integer greater than zero, the value of the Smarandache function Sen) is the smallest integer m such that n divides m!. He closes the paper by askin...

We study differential-geometrical structure of an information manifold equipped with a divergence function.A divergence function generates a Riemannian metric and furthermore it provides a symmetric third-order tensor,when the divergence is asymmetric. This induces a pair of affine connections dually coupled to each other withrespect to the Riemannian metric. This is the arising eme...

The purpose of this paper is to state a set of axioms for plane geometry which do not use any quantifiers, but only constructive operations. The relevant definitions and general theorems are stated; for reasons of space the proofs are only sketched. Quantifier-free arithmetic and quantifier-free algebra have been the subjects of several investigations, beginning at least with the early importan...

We study differential-geometrical structure of an information manifold equipped with a divergence function. A divergence function generates a Riemannian metric and furthermore it provides a symmetric third-order tensor, when the divergence is asymmetric. This induces a pair of affine connections dually coupled to each other with respect to the Riemannian metric. This is the arising emerged from...