Experimental Mathematics. 399 



But A6 = 0A multiplied by the circular measure of the 

 angle AOB, which is 1/10000U0. Hence writing m to denote 

 one million, we have 



OB = l + l/m. 



Similarly OC = OB + Bc. 



But Bc = OBxl/m. 



Therefore OC = OB(l + 1/m) = (1 + 1/m) 2 . 



Fig-. 3. 







In this way we can write down the values of the radius 

 vector as it proceeds from OA to Oe : — 



The radius vector is 



1 



(1 + 1/ro) 



(1 + 1/m) 2 



(1-fl/m) 3 



(l + l/???) m 



When the angle is 







1/m 



2/m 

 3/m 



mjm, or 1 



By calculation, the value of (l + l/m) m is found to be 

 2*7 .. , and by direct measurement with a foot-rule we arrive 



2 E 2 



