Evolutes

This: http://uk.arxiv.org/PS_cache/math/pdf/0412/0412421v1.pdf attempts to explain evolutes as the curve traced out by the centers of curvature. However, my differential geometry book actually says that involutes are curves on the surface traced by the tangent lines of the curve that are orthogonal to the tangent line that traced this surface, and that an evolute is the inverse of the involute (i. e. a curve is the evolute of the other when an involute of the other is the curve), which yields infinitely many evolutes. So is this online textbook fail?