scholarly journals Essays on the Theory of Numbers I. Continuity and Irrational Numbers II. The Nature and Meaning of Numbers

Nature ◽  
1901 ◽  
Vol 64 (1659) ◽  
pp. 374-374
Author(s):  
M.
Keyword(s):  
Irrational Numbers ◽  
Theory Of Numbers

scholarly journals Elementary methods in the theory of numbers

1939 ◽  
Vol 31 ◽  
pp. xvi-xxiii
Author(s):  
S. A. Scott
Keyword(s):  
Number Theory ◽  
Positive Integer ◽  
Exponential Function ◽  
Monotone Sequence ◽  
Binomial Theorem ◽  
Irrational Numbers ◽  
Early Stages ◽  
Elementary Methods ◽  
Usual Notation ◽  
Theory Of Numbers

§ 1. The importance of proving inequalities of an essentially algebraic nature by “elementary” methods has been emphasised by Hardy (Prolegomena to a Chapter on Inequalities), and by Hardy, Littlewood and Polya (Inequalities). The object of this Note is to show how some of the results in the early stages of Number Theory can be obtained by making a minimum appeal to irrational numbers and the notion of a limit. We use the elementary notion of a logarithm to a base “a” > 1, and make no appeal to the exponential function. The Binomial Theorem is only used for a positive integer index. Our minimum appeal rests in the assumption that a bounded monotone sequence tends to a limit. We adopt throughout the usual notation. Finally, it need scarcely be added that the methods employed are not claimed to be new.

New Ideas for the Classroom: Decimals and duodecimals, .333 … or .400

1959 ◽  
Vol 52 (7) ◽  
pp. 570-571
Author(s):  
Robert C. McLean
Keyword(s):  
Irrational Numbers ◽  
Common Fractions ◽  
New Ideas ◽  
Theory Of Numbers

When the theory of numbers professor enters upon the discussion of never-ending decimals, he carefully points out that irrational numbers give non-repeating digits and that common fractions give repeating digits. A common example of this latter condition is one-third, well known as .33333….

scholarly journals Incommensurate Numbers, Continued Fractions, and Fractal Immittances

1988 ◽  
Vol 43 (11) ◽  
pp. 943-955 ◽  
Author(s):  
A. Lakhtakia ◽  
R. Messier ◽  
V. V. Varadan ◽  
V. K. Varadan
Keyword(s):  
Network Structure ◽  
Continued Fractions ◽  
Rough Surfaces ◽  
Thick Films ◽  
Irrational Numbers ◽  
Theory Of Numbers

Abstract Continued fractions have a rich tradition in the theory of numbers; e.g., non-terminating con­ tinued fractions represent irrational numbers. It will be shown that a class of continued fractions possess the property of self-referential decomposition, and their interpretation in the form of non-terminating ladder circuits gives rise to fractal immittances with potential analogies to rough surfaces, thin cermet films, as well as to the internal void network structure of thick films.

The elliptic products of Jacobi and the theory of linear congruences

1926 ◽  
Vol 23 (4) ◽  
pp. 337-355
Author(s):  
P. A. MacMahon
Keyword(s):  
Elliptic Functions ◽  
Linear Congruences ◽  
Image Position ◽  
Theory Of Numbers

In the application of Elliptic Functions to the Theory of Numbers the two formulae of Jacobiare of great importance.

Teaching Irrational Numbers Through Trigonometry

Resonance ◽  
2021 ◽  
Vol 26 (6) ◽  
pp. 813-827
Author(s):  
Sameen Ahmed Khan
Keyword(s):  
Irrational Numbers

A Memoir in the Theory of Numbers

1887 ◽  
Vol 9 (2) ◽  
pp. 162 ◽  
Author(s):  
Arthur S. Hathaway
Keyword(s):  
Theory Of Numbers

scholarly journals On subrecursive representability of irrational numbers

Computability ◽  
2017 ◽  
Vol 6 (3) ◽  
pp. 249-276 ◽  
Author(s):  
Lars Kristiansen
Keyword(s):  
Irrational Numbers
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