Primitive Pythagorean triples (PPT) may be put into different equivalence classes using residues with respect to primes. We show that the probability that the smaller odd number associated with the PPT triple is divisible by prime p is 2/(p+1). We have determined the autocorrelation function of the Baudhāyana sequences obtained from the residue classes and we show these sequences have excellent...

This paper presents new properties of Primitive Pythagorean Triples (PPT) that have relevance in applications where events of different probability need to be generated and in cryptography.

Javanese context is rich of phenomena potentially used as a starting point to learn mathematics. On the other hand, Indonesian students’ performance in PISA consistently low due small number PISA-like problems which can be foster mathematical literacy measured PISA. Therefore, this research aims develop set using targeted for 8 th -grade students Junior High School. It development study Plomp’s...

The Gibbs distribution of statistical physics is an exponential family of probability distributions, which has a mathematical basis of duality in the form of the Legendre transformation. Recent studies of complex systems have found lots of distributions obeying the power law rather than the standard Gibbs type distributions. The Tsallis q-entropy is a typical example capturing such phenomena. W...

Real analysis is a rigorous study of the (hopefully familiar) objects from calculus: the real numbers, functions, limits, continuity, derivatives, sequences, series, and integrals. While you are likely quite familiar with computing with these objects, this course will focus on developing the theoretical foundation for the definitions, theorems, formulas, and algorithms that you are used to usin...

The Pythagorean fuzzy set is an extension of the intuitionistic used to handle uncertain circumstances in various decisions making problems. Group theory a mathematical technique for dealing with problems symmetry. This study deals group theory. In this article, we characterize notion subgroup and examine algebraic properties concept. An extensive on cosets subgroup, normal subgroups performed....

Alternating current circuits are one of the physics taught in senior high school. (AC) material related to mathematical equations so that study this students must have good abilities. This research will discuss improvement test results for AC circuit material, especially RL series, RC and RLC series using an alternative method form Pythagorean theorem on impedance voltage equations. is because ...

In the paper, Pythagorean-hodograph cycloidal curves as an extension of PH cubics are introduced. Their properties are examined and a constructive geometric characterization is established. Further, PHC curves are applied in the Hermite interpolation, with closed form solutions been determined. The asymptotic approximation order analysis carried out indicates clearly which interpolatory curve s...

We prove for a large class of fields $F$ that every proper finite extension $F_{pyth}$, the pythagorean closure $F$, is not field. This contains number and are finitely generated transcendence degree at least one over some subfield $F$.