[sci.math] Continued fractions

jeff@ics.uci.edu (Jeff Erickson) (03/16/91)

rthomson@mesa.dsd.es.com (Rich Thomson) writes:

| I think it turns out that non-rational numbers have a continued
| fraction expansion that is eventually periodic (i.e. after a finite
| number of coefficients in the expansion, a block of coefficients
| repeats infinitely), while all rational numbers have a finite
| continued fraction expansion.

Only (and all) roots of quadratic equations have periodic continued
fraction expansions.  Numbers like 2^(1/3), log(2), and pi do not.

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