scholarly journals Calculation of π with a needle

2019 ◽  
Vol 103 (556) ◽  
pp. 111-116
Author(s):  
Athina Lorentziadi
Keyword(s):  
18Th Century ◽  
Irrational Number ◽  
Polynomial Equation ◽  
Transcendental Number ◽  
Mathematical Problems

The number πis perhaps the most famous irrational number. This constant is equal to the ratio of the circumference of a circle to its diameter. One of the most well-known mathematical problems of antiquity, which is related to π, is how to construct by using a ruler and compasses a square which has the same area as a circle. This particular problem cannot be solved, due to the fact that π is a transcendental number, which means that it cannot be obtained as the root of a polynomial equation with rational coefficients. It was Euler in the 18th century who established the notation π.

scholarly journals ON THE BITS COUNTING FUNCTION OF REAL NUMBERS

2008 ◽  
Vol 85 (1) ◽  
pp. 95-111 ◽  
Author(s):  
TANGUY RIVOAL
Keyword(s):  
Lower Bounds ◽  
Irrational Number ◽  
Counting Function ◽  
Fibonacci Sequence ◽  
Difficult Problem ◽  
Transcendental Number ◽  
Algebraic Numbers ◽  
Real Numbers ◽  
Binary Expansion ◽  
Multiplicative Constant

AbstractLet Bn(x) denote the number of 1’s occurring in the binary expansion of an irrational number x>0. A difficult problem is to provide nontrivial lower bounds for Bn(x) for interesting numbers such as $\sqrt {2}$, e or π: their conjectural simple normality in base 2 is equivalent to Bn(x)∼n/2. In this article, amongst other things, we prove inequalities relating Bn(x+y), Bn(xy) and Bn(1/x) to Bn(x) and Bn(y) for any irrational numbers x,y>0, which we prove to be sharp up to a multiplicative constant. As a by-product, we provide an answer to a question raised by Bailey et al. (D. H. Bailey, J. M. Borwein, R. E. Crandall and C. Pomerance, ‘On the binary expansions of algebraic numbers’, J. Théor. Nombres Bordeaux16(3) (2004), 487–518) concerning the binary digits of the square of a series related to the Fibonacci sequence. We also obtain a slight refinement of the main theorem of the same article, which provides a nontrivial lower bound for Bn(α) for any real irrational algebraic number. We conclude the article with effective or conjectural lower bounds for Bn(x) when x is a transcendental number.

scholarly journals Jak pokazać to, czego pokazać nie można? O obrazowaniu liczb niewymiernych

2020 ◽  
Vol 15 (3) ◽  
pp. 17-30
Author(s):  
Jakub Jernajczyk
Keyword(s):  
Irrational Number ◽  
Golden Ratio ◽  
Visual Artists ◽  
Geometrical Method ◽  
Square Roots ◽  
Visual Imagination ◽  
Starting Point ◽  
Mathematical Problems ◽  
Number Π

In this article, I would like to draw attention to the cognitive potential of an image, showing how significant the role of visual imagination in mathematics is. I will focus here mainly on the possibilities of visualizing irrational numbers.Our starting point is the intuitive case of the square root of two, observed in the diagonal of a square. We will also discuss a simple, geometrical method of constructing the square roots of all integers. Next, we move over to the golden ratio, hidden in a regular pentagon. We will use a looped, endless animation to visualize the irrational number φ. Then we will have a closer look at the famous number π and discuss two different attempts to find its visual representation. In the last two sections of the article, we consider the possibility of indicating rational and irrational real numbers and also grasp the whole set of real numbers.All the issues discussed in this article have inspired visual artists to create artworks that can help to understand relatively advanced mathematical problems.

EPITAFIES OF THE RELATIVES OF HADJI IBRAHIM AL-URADI AS A SOURCE ON THE BIOGRAPHY OF THE SCIENTIST AND ON THE HISTORY OF GIDATL

2017 ◽  
Vol 13 (4) ◽  
pp. 13-21
Author(s):  
Sh M Khapizov ◽  
M G Shekhmagomedov
Keyword(s):  
18Th Century ◽  
Medieval History ◽  
Historical Sources ◽  
The Past ◽  
Arabic Script ◽  
History Of ◽  
History Of Culture ◽  
The Look ◽  
Cultural Monuments ◽  
Written Sources

The article is devoted to the study of inscriptions on the gravestones of Haji Ibrahim al-Uradi, his father, brothers and other relatives. The information revealed during the translation of these inscriptions allows one to date important events from the history of Highland Dagestan. Also we can reconsider the look at some important events from the past of Hidatl. Epitaphs are interesting in and of themselves, as historical and cultural monuments that needed to be studied and attributed. Research of epigraphy data monuments clarifies periodization medieval epitaphs mountain Dagestan using record templates and features of the Arabic script. We see the study of medieval epigraphy as one of the important tasks of contemporary Caucasian studies facing Dagestani researchers. Given the relatively weak illumination of the picture of events of that period in historical sources, comprehensive work in this direction can fill gaps in our knowledge of the medieval history of Dagestan. In addition, these epigraphs are of great importance for researchers of onomastics, linguistics, the history of culture and religion of Dagestan. The authors managed to clarify the date of death of Ibrahim-Haji al-Uradi, as well as his two sons. These data, the attraction of written sources and legends allowed the reconstruction of the events of the second half of the 18th century. For example, because of the epidemic of plague and the death of most of the population of Hidatl, this society noticeably weakened and could no longer maintain its influence on Akhvakh. The attraction of memorable records allowed us to specify the dates of the Ibrahim-Haji pilgrimage to Mecca and Medina, as well as the route through which he traveled to these cities.

STUDI DESKRIPTIF MINAT CALON GURU SEKOLAH DASAR TERHADAP PENGGUNAAN ALAT PERAGA MATEMATIKA SETELAH PERKULIAHAN MEDIA DAN MODEL PEMBELAJARAN MATEMATIKA SD

2015 ◽  
Vol 8 (1) ◽  
pp. 19
Author(s):  
Isna Rafianti ◽  
Etika Khaerunnisa
Keyword(s):  
Elementary Teachers ◽  
Elementary Mathematics ◽  
Mathematics Learning ◽  
Learning Model ◽  
Prospective Elementary Teachers ◽  
Descriptive Research ◽  
Learning Mathematics ◽  
Mathematical Problems ◽  
The Subject ◽  
Object Of Study

This research is motivated by the lack of interest of teachers in the use of props in the process of learning mathematics in elementary school. In accordance with the demands of the curriculum in 2013 and supported by the developed learning theory, learning mathematics is abstract object of study, students need an intermediary that props math-ematics, so that students can more easily understand the concepts that will be pre-sented, and in the end it can deliver students to solve mathematical problems, not only that proposed by the teacher but also the problems in life. The purpose of this study was to determine the interest of prospective elementary teachers on the use of props mathematics after getting lectures media and elementary mathematics learning model. By knowing the interest of prospective elementary teachers will be developed further realization of the state of the subject being studied. The method used is descriptive research, then the instruments used were questionnaires and interviews. The results of this study stated that the interest of prospective elementary teachers on the use of props after attending lectures media and elementary mathematics learning model is high over-all with a percentage of 76.70%.Keywords : Interest, Props Mathematics

Nature, poetry and medicine in late 18th century England: a unified perspective of Erasmus Darwin

1976 ◽  
Vol 7 (4) ◽  
pp. 537-537
Author(s):  
M. McNEIL
Keyword(s):  
18Th Century ◽  
Human Society ◽  
Nature Poetry ◽  
Medicine And Philosophy ◽  
Late 18Th Century ◽  
Medical Theory ◽  
Lunar Society Of Birmingham ◽  
Organizational Principles ◽  
Century Science ◽  
Erasmus Darwin

Erasmus Darwin was the focus and embodiment of provincial England in his day. Renowned as a physician, he spent much of his life at Lichfield. He instigated the founding of the Lichfield Botanic Society, which provided the first English translation of the works of Linnaeus, and established a botanic garden; the Lunar Society of Birmingham; the Derby Philosophical Society; and two provincial libraries. A list of Darwin's correspondents and associates reads like a "who's who" of eighteenth century science, industry, medicine and philosophy. His poetry was also well received by his contemporaries and he expounded the evolutionary principles of life. Darwin can be seen as an English equivalent of Lamarck, being a philosopher of nature and human society. His ideas have been linked to a multitude of movements, including the nosological movement in Western medicine, nineteenth century utilitarianism, Romanticism in both Britain and Germany, and associationist psychology. The relationships between various aspects of Darwin's interests and the organizational principles of his writings were examined. His poetical form and medical theory were not peripheral to his study of nature but intrinsically linked in providing his contemporaries with a panorama of nature. A richer, more integrated comprehension of Erasmus Darwin as one of the most significant and representative personalities of his era was presented.

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