Name ____________________________________
   From Euclid to Spigotry
Assignment 2 (outlines 2 and 3)
Last modified: Sept 14, 2004
You can do everything on this piece of paper and hand it in. 
1. Here are line segments whose lengths are 1, a, and b

On the axes below, use your compass and straightedge to construct the two solutions to the equation 

2. Divide  by  and express the answer in the form . Write the answer below. Use may use Mathematica if you like.

3. Construct a line segment whose length is  (relative to the unit length shown). You can use the Pythagorean theorem to get  , then use the circle construction from Bold to finish the job. Think how hard it would be to get 10 decimal digits of this number without a calculator!

4. Use high-school algebra to find an equation that is satisfied by x=.  You will have to square twice; so the equation will involve .  Use Mathematica to find all four solutions to this equation.  You will have to use //FullSimplify to see the answer that you expect!  Write the equation and its four solutions below, or attach a printout of your Mathematica notebook.