Book Review: Irrational numbers

On Irrational and Transcendental Numbers

Unsymmetrical Approximation of Irrational Numbers

1 A 1 < £ < , 5B B SB so that we have the classical theorem of Hurwitz. For other values of r, approximations from both sides are permitted, but the errors allowed on the two sides are different; hence the term unsymmetrical approximation. The result here was new, and is so related to Hurwitz's inequality that one side is strengthened and the other weakened. Notice that the result for r > l is ...

Representing numbers: prime and irrational

This article draws an analogy between prime and irrational numbers with respect to how these numbers are defined and how they are perceived by learners. Excerpts are presented from two research studies: a study on understanding prime numbers by pre-service elementary school teachers and a study on understanding irrational numbers by pre-service secondary school teachers. Considering the results...

Continued Fractions, Fibonacci Numbers, and Some Classes of Irrational Numbers

In this paper we define an equivalence relation on the set of positive irrational numbers less than 1. The relation is defined by means of continued fractions. Equivalence classes under this relation are determined by the places of some elements equal to 1 (called essential 1’s) in the continued fraction expansion of numbers. Analysis of suprema of all equivalence classes leads to a solution wh...

Some Theorems Connected with Irrational Numbers.

For testing the importance of the lymphoid tissue in natural immunity we can only compare the percentage of takes in X-rayed and normal animals inoculated with the same cancer. This has been done with a variety of different cancers and a large series of animals. The average number of takes in the X-rayed animals was 94%, while in the untreated animals only 32% of those inoculated grew the cance...