Journal of Multidisciplinary Engineering Science and Technology (JMEST), 2020
Since antiquity, mathematics has been fundamental to advances in science, engineering, and philos... more Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. Mathematics and humanity itself are nearly at the same age. Sumerian and Babylonian mathematics was based on a sexegesimal, or base 60, numeric system. It is thought that the Egyptians introduced the earliest fully-developed base 10 numeration system at least as early as 2700 BCE. We now use the Indu-Arab systems in educations books, integer bases for computer science , binary systems, or others [18]. Among the different possible representations of real numbers in a real (or complex) base , the-expansion introduced by Renyi´ is very important for advance in different maths fields. The present paper focuses onexpansion of an algebraic number in an algebraic base , with a point of view from Diophantine approximation. We are going to study the point which are called the sets of badly approximable number. They have an important role in classical diophantine approximation [1]. For the set (,) = { ∈ | ≥ () ≥ } From now and all this papers beta numbers are Pisot or Salem numbers. The algebraic numbers > and their conjugate are less or iqual in modul to 1. The expansions of 1 in base turns out to be crucial for characterizing the − shift. The closure of the − shift is totally determined by the expansions of 1. Some results are to be given on this papers.
FIRST INTERNATIONAL CONFERENCE ON NATURAL SCIENCES, MATHEMATICS AND TECHNOLOGY (ICNSMT-2023), 2023
When we think geometry as a science we associated that with the name of mathematician of the anci... more When we think geometry as a science we associated that with the name of mathematician of the ancient Greek, Euclid (around 300 B.C). Geometry, one of the oldest branch of math so named at least since Plato's time. The concept came from practice then follow its development into a rigorous abstract science by the Greek philosophers, until the rich period with more and more sophisticated problems and methods in the later Greek and Arab period. Euclid is referred to as the "Father of Geometry", and he wrote s the most important and successful mathematical textbook of all time, the "Stoicheion" or "Elements", which represents the culmination of the mathematical revolution which had taken place in Greece up to that time. Bolyai, came to the radical conclusion that it was in fact possible to have consistent geometries that were independent of the parallel postulate. In the early 1820s, Bolyai explored what he called "imaginary geometry" (now known as hyperbolic geometry). Mathematicians recognized during their 1875-1925 crisis that a proper understanding of irregularity or fragmentation (as of regularity and connectedness) cannot be satisfied with defining dimension as a number of coordinates. The first step of a rigorous analysis is taken by Cantor in his June 20, 1877, letter to Dedekind, the next step by Peano in 1890, and the final steps in the 1920's. Benoit B. Mandlebrot felt that Euclidean geometry was not satisfactory as a model for natural objects. Here we give some elements of story to development of geometry.
Journal of Multidisciplinary Engineering Science and Technology (JMEST), 2020
Since antiquity, mathematics has been fundamental to advances in science, engineering, and philos... more Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. Mathematics and humanity itself are nearly at the same age. Sumerian and Babylonian mathematics was based on a sexegesimal, or base 60, numeric system. It is thought that the Egyptians introduced the earliest fully-developed base 10 numeration system at least as early as 2700 BCE. We now use the Indu-Arab systems in educations books, integer bases for computer science , binary systems, or others [18]. Among the different possible representations of real numbers in a real (or complex) base , the-expansion introduced by Renyi´ is very important for advance in different maths fields. The present paper focuses onexpansion of an algebraic number in an algebraic base , with a point of view from Diophantine approximation. We are going to study the point which are called the sets of badly approximable number. They have an important role in classical diophantine approximation [1]. For the set (,) = { ∈ | ≥ () ≥ } From now and all this papers beta numbers are Pisot or Salem numbers. The algebraic numbers > and their conjugate are less or iqual in modul to 1. The expansions of 1 in base turns out to be crucial for characterizing the − shift. The closure of the − shift is totally determined by the expansions of 1. Some results are to be given on this papers.
FIRST INTERNATIONAL CONFERENCE ON NATURAL SCIENCES, MATHEMATICS AND TECHNOLOGY (ICNSMT-2023), 2023
When we think geometry as a science we associated that with the name of mathematician of the anci... more When we think geometry as a science we associated that with the name of mathematician of the ancient Greek, Euclid (around 300 B.C). Geometry, one of the oldest branch of math so named at least since Plato's time. The concept came from practice then follow its development into a rigorous abstract science by the Greek philosophers, until the rich period with more and more sophisticated problems and methods in the later Greek and Arab period. Euclid is referred to as the "Father of Geometry", and he wrote s the most important and successful mathematical textbook of all time, the "Stoicheion" or "Elements", which represents the culmination of the mathematical revolution which had taken place in Greece up to that time. Bolyai, came to the radical conclusion that it was in fact possible to have consistent geometries that were independent of the parallel postulate. In the early 1820s, Bolyai explored what he called "imaginary geometry" (now known as hyperbolic geometry). Mathematicians recognized during their 1875-1925 crisis that a proper understanding of irregularity or fragmentation (as of regularity and connectedness) cannot be satisfied with defining dimension as a number of coordinates. The first step of a rigorous analysis is taken by Cantor in his June 20, 1877, letter to Dedekind, the next step by Peano in 1890, and the final steps in the 1920's. Benoit B. Mandlebrot felt that Euclidean geometry was not satisfactory as a model for natural objects. Here we give some elements of story to development of geometry.
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