Exercise 3:
Pythagorean Triples

Instructions:
You may email your notebook as an attachment to me at helmut@math.utep.edu. Do only send unevaluated notebooks, do NOT send evaluated notebooks!
Alternatively you may post your notebook on your webpage and let me know that you have done so.

A Pythagorean Triple is a triple (a,b,c) of positive integers such that (a^2)+(b^2)=(c^2), such that a≤b≤c, and such that gcd (a,b,c)=1. 
a=3, b=4, c=5 is the "smallest" Pythagorean Triple. It is known since antiquity that there are infinitely many P.T.'s.  
1.) Find all P.T.'s  for which 1≤a≤b≤200.
2.) Sort their tangents a/b by size and plot them. A convenient command for this is "ListPlot". Do you notice any irregularities in the distribution of the tangents?

ListPlot[{3, 6, 2, 4, -1, π, 6}, 
      PlotStyle -> AbsolutePointSize[8]];