In this article, the author offers two well-known mathematical images--that of a dot moving around a circle; and that of the tens chart--and considers their power for developing mathematical thinking. In his opinion, these images each contain the essence of a particular topic of mathematics. They are contrasting images in the sense that they deal with quite different aspects of the curriculum, the first being trigonometry and the second being number. They are also different in another way: the former has within it the essence of the mathematics (trigonometry) to which it refers. In this sense it is a way of looking directly at some geometry involved with trigonometry. The second image uses the geometric property of position as a pedagogic tool to stress the structure within number names. In this sense it is a pedagogic construct. (Contains 13 figures.)