Name __________________________________
   From Euclid to Spigotry
Assignment 18 (outline 14)
Last modified: September 14, 2004
1. Calculate the complex number (5 + 2i)2 (41+i)
and explain why the result implies that  
2. Invent an arctangent identity that is different from any of the ones on the one-page handout from the Pi Source Book and attach a Mathematica printout showing its use to calculate 200 decimal places of p. All you have to do is find complex numbers whose product is proportional to 1+i.

3. According to Euler, p = 4 arctan 1/2 + 4 arctan 1/3
You can evaluate both of these by using the series
arctan x =  where .
Alternatively, arctan x = 
For both series, compute the first term exactly.  Then for the rest of the series, find one 
geometric series that is smaller and one that is larger, in the manner of the infinite series handout, topic 4c. This should give you one number that is less than p and one that is greater than p.