We study Kauffman's model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The folded ribbonlength is the length to width ratio of such a ribbon knot. We give upper bounds on the folded ribbonlength of 2-bridge, (2, p) torus, twist, and pretzel knots, and these upper bounds turn out to be linear in crossing number. We give a new way to fold (p, q) torus knots, and show that their folded ribbonlength is bounded above by p + q. This means, for example, that the trefoil knot can be constructed with a folded ribbonlength of 5. We then show that any (p, q) torus knot K has a constant c > 0, such that the folded ribbonlength is bounded above by c • Cr(K) 1/2 , providing an example of an upper bound on folded ribbonlength that is sub-linear in crossing number.
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