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We construct a class of quadratic irrationals having continued fractions ofperiod $n\geq2$ with "small" partial quotients for which certain integermultiples have continued fractions of period $1$, $2$ or $4$ with "large"partial quotients. We then show that numbers in the period of the new continuedfraction are simple functions of the numbers in the periods of the originalcontinued fraction. We give generalizations of some of the continued fractionsand show that polynomials arising from the generalizations are related toChebyshev and Fibonacci polynomials. We then show that some of thesepolynomials have a hyperbolic root distribution.

Multiples of long period small element continued fractions to short period large elements continued fractions