problem0():
  Estimate the square root of pi.
5.15707963267949
2.883130095853957
1.9863883041004537
1.7839742445187232
1.7724910486031316
1.7724538512958334
1.7724538509055159

  Exact value =  1.7724538509055159

problem1():
  E=mc^2.
3.1456431255788614e+17  =  3.5 * 299792458 **2

problem2():
  Body Mass Index.
  Sandy's BMI is  28.02768166089965
  Dale's BMI is  21.76870748299319

problem3():
  nchoosek
6 choose 2  =  15
60 choose 20  =  4191844505805495
600 choose 200  =  250601778322140280500561677051322883520255102508793389473094343332441398315528846878026090182866148274621477126087990864486283260622128340138769443055475567389095596

problem4():
  mandelbrot

starting point =  (-0.8+0.1j)
0.806225774829855
0.18027756377319942
0.7840001594387593
0.23115030967762623
0.7737931503522865
0.26245883986192126
0.769946755738411
0.2845202961749073
0.7705537157156268
0.30072355973052173
0.774808107834127

starting point =  (-0.75+0.4j)
0.85
0.4009441981124057
0.8593068118629473
0.6741969741097801
0.9284795889921212
1.172602703170592
1.2941629291502168
2.5246796993056617
5.653735717023719
32.0743487210876
1029.3713274436163

problem5():
  Heron's triangle area formula.
  Area =  25.298221281347036

  Illegal square root!

problem6():
  The dice problem.
  a =  2   b =  6   c =  3
  a =  3   b =  5   c =  1

problem7():
  Repeatedly fold a piece of paper.
  k =  42

problem8():
  Earth surface area.
  Estimate for Earth surface area =  510065621724078.94

problem9():
  Estimate exp(4).
  Exact value of exp(4) =  54.598150033144236
  Estimate  0  =  1.0   error =  53.598150033144236
  Estimate  1  =  5.0   error =  49.598150033144236
  Estimate  2  =  13.0   error =  41.598150033144236
  Estimate  3  =  23.666666666666664   error =  30.931483366477572
  Estimate  4  =  34.33333333333333   error =  20.264816699810908
  Estimate  5  =  42.86666666666666   error =  11.731483366477576
  Estimate  6  =  48.55555555555555   error =  6.042594477588686
  Estimate  7  =  51.8063492063492   error =  2.7918008267950327
  Estimate  8  =  53.43174603174603   error =  1.166404001398206
  Estimate  9  =  54.15414462081129   error =  0.4440054123329489