26 Transactions Tennessee Academy of Science 



SOME LINK MOTIONS-HOW TO DRAW 

 A STRAIGHT LINE 



BY SAMUEL M. BARTON, UNIVERSITY OF THE SOHTH. 



[Read before the Academy, November 27, 1914.] 



The geometrician Euclid based his geometry on certain postulates. 

 These postulates required that we should be able to draw straight 

 lines and circles. By Euclid and his followers no demonstration 

 was allowed that required any other construction than such as could 

 be effected by straight lines and circles. In other words, the Greek 

 geometer could use a straight edge for drawing a straight line and 

 a "string" for describing a circle. With such limitations, as is well 

 known, some of the problems proposed by the Greeks were insoluble. 

 These postulates assume that a straight line can be drawn, and that 

 a circle can be drawn. Now, can they? Describing a circle is the 

 simpler of the two problems, assuming that we can keep the point 

 of a pencil (say) at a constant distance from a fixed point called 

 the center. This may be practically effected by employing a string 

 or wire that is not easily stretched, or a bar, or link, fixed to a plane 

 table by a pin about Avhich it can freely turn, with a small hole at 

 some other point to take the point of a pencil. This might be termed 

 the simplest form of link motion, where one link is employed. 



The other problem — to draw a straight line — is not so easy. It 

 is doubtless commonly thought that it is a very simple operation to 

 draw a straight line. All we have to do is to take a ruler or straight 

 edge and hiy it fiat on the paper, and pass a pencil along its edge, 

 and, behold, we have a straight line. But how do we know that the 

 edge of our ruler is straight? Or, if it is straight, how was it made 

 straight? This is exactly similar to the method of drawing a circle 

 by running the point of a pencil around the edge of a silver dollar 

 or some circuhu phile, by which operation we can not be sure that 

 we get an exact circle unless we know thai the edge of the coin or 

 plate is a true ciifle. 



Ihe objecl dI lliis paper is to call allcniion hi soidc link-motions 

 bv means ol uliidi an accurate straight line can he drawn. These 

 methods arc iujI new. hut one so seldom sees any reference lo them 



