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ERIC Number: EJ819169
Record Type: Journal
Publication Date: 2008-Dec
Pages: 10
Abstractor: As Provided
Reference Count: 0
ISSN: ISSN-0268-3679
Pythagorean Approximations and Continued Fractions
Peralta, Javier
Teaching Mathematics and Its Applications: An International Journal of the IMA, v27 n4 p200-209 Dec 2008
In this article, we will show that the Pythagorean approximations of [the square root of] 2 coincide with those achieved in the 16th century by means of continued fractions. Assuming this fact and the known relation that connects the Fibonacci sequence with the golden section, we shall establish a procedure to obtain sequences of rational numbers converging to different algebraic irrationals. We will see how approximations to some irrational numbers, using known facts from the history of mathematics, may perhaps help to acquire a better comprehension of the real numbers and their properties at further mathematics level.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A