84 CHAPTER 4 although correspondingly more expensive to produce, than a printed scale. Cutting along the horizontal lines for 0 and 10 and rolling the paper round so that these lines coincide gives us a screw thread. Such a screw forms the basis of micrometers and the fine adjustment mechanisms used in instruments of all kinds. 4.6 Similar Triangles and the Sector Another important topic is that of similar triangles: two triangles are similar when the sets of angles are equal. When this happens, the lengths of corresponding sides are related by a fixed multi- plication factor. Hence, similarity really has a lot to say about scale. One classical mathematical instrument which is based on the properties of similar triangles is the sector, which is an instru- ment consisting of two rulers of equal length that are joined by a hinge. A number of scales are drawn on the instrument facili-