becomes very large, and finds that the little space that is "jumped" by the inner polygon becomes smaller and smaller. He writes: Therefore a larger polygon having a thousand sides passes over and measures a straight line equal to its perimeter, while at the same time the smaller one passes an approximately equal line, but one interruptedly composed of a thousand little particles equal to its thousand sides with a thousand little void spaces interposed — for we may call these "void" in relation to the thousand linelets touched by the sides of the polygon. Since a circle is just the limit in which the number of faces on the polygon becomes infinite, Galileo finds that Aristotle's wheel contains material that is filled with infinitesimal spaces or "voids", and that "the interposed voids are not quantified, but are infinitely many". This leads him to conclude that a belief in atoms – in the sense that matter is "composed of infinitely many unquantifiable atoms" – is sufficient to explain the phenomenon. Gilles de Roberval (1602–1675) is also associated with this analysis. In the 19th century Bernard Bolzano discussed Aristotle's wheel in The Paradoxes of the Infinite (1851), a book that influenced Georg Cantor and subsequent thinkers about the mathematics of infinity. Bolzano observes that there is a bijection between the points of any two similar arcs, which can be implemented by drawing a radius, remarking that the history of this apparently paradoxical fact dates back to Aristotle. In the 20th century The author of Mathematical Fallacies and Paradoxes uses a dime glued to a half-dollar (representing smaller and larger circles, respectively) with their centers aligned and both fixed to an axle, as a model for the paradox. He writes: This is the solution, then, or the key to it. Although you are careful not to let the half-dollar slip on the tabletop, the “point” tracing the line segment at the foot of the dime is both rotating and slipping all the time. It is slipping with respect to the tabletop. Since the dime does not touch the table top, you do not notice the slipping. If you can roll the half-dollar along the table and at the same time roll the dime (or better yet the axle) along a block of wood, you can actually observe the slipping. If you have ever parked too close to the curb, you have noticed