#! /usr/bin/env python3
#
def problem0 ( ):

#*****************************************************************************80
#
## problem0(): Estimate the square root of pi.
#
  from math import pi
  from math import sqrt

  print ( '' )
  print ( 'problem0():' )
  print ( '  Estimate the square root of pi.' )
  
  x = 10.0
  x = 0.5 * ( x + pi / x ); print ( x )
  x = 0.5 * ( x + pi / x ); print ( x )
  x = 0.5 * ( x + pi / x ); print ( x )
  x = 0.5 * ( x + pi / x ); print ( x )
  x = 0.5 * ( x + pi / x ); print ( x )
  x = 0.5 * ( x + pi / x ); print ( x )
  x = 0.5 * ( x + pi / x ); print ( x )
  print ( '' )
  print ( '  Exact value = ', sqrt ( pi ) )
  return

def problem1 ( ):

#*****************************************************************************80
#
## problem1(): Energy equivalent.
#
  print ( '' )
  print ( 'problem1():' )
  print ( '  E=mc^2.' )
  m = 3.5
  c = 299792458
  E = m * c**2
  print ( E, ' = ', m, '*', c,'**2' )
  return
  
def problem2 ( ):

#*****************************************************************************80
#
## problem2(): BMI.
#
  print ( '' )
  print ( 'problem2():' )
  print ( '  Body Mass Index.' )
  
  w_lb = 180
  h_in = 5 * 12 + 8
  w_kg = w_lb * 0.45
  h_m = h_in * 0.025
  BMI = w_kg / h_m**2
  print ( '  Sandy\'s BMI is ', BMI )

  w_lb = 120
  h_in = 5 * 12 + 3
  w_kg = w_lb * 0.45
  h_m = h_in * 0.025
  BMI = w_kg / h_m**2
  print ( '  Dale\'s BMI is ', BMI )
  
  return
  
def problem3 ( ):

#*****************************************************************************80
#
## problem3(): nchoosek.
#
  from math import factorial
  
  print ( '' )
  print ( 'problem3():' )
  print ( '  nchoosek' )
  
  n = 6
  k = 2
  nchoosek = factorial ( n ) // factorial ( n - k ) // factorial ( k )
  print ( n, 'choose', k, ' = ', nchoosek )

  n = 60
  k = 20
  nchoosek = factorial ( n ) // factorial ( n - k ) // factorial ( k )
  print ( n, 'choose', k, ' = ', nchoosek )

  n = 600
  k = 200
  nchoosek = factorial ( n ) // factorial ( n - k ) // factorial ( k )
  print ( n, 'choose', k, ' = ', nchoosek )

  return
  
def problem4 ( ):

#*****************************************************************************80
#
## problem4(): mandelbrot.
#
  from math import factorial
  
  print ( '' )
  print ( 'problem4():' )
  print ( '  mandelbrot' )
  
  c = - 0.80 + 0.1j
  print ( '' )
  print ( 'starting point = ', c )
  z = c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  
  c = - 0.75 + 0.4j
  print ( '' )
  print ( 'starting point = ', c )
  z = c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )
  z = z**2 + c; print ( abs ( z ) )

  return

def problem5 ( ):

#*****************************************************************************80
#
## problem5(): Heron's formula.
#
  from math import sqrt
  
  print ( '' )
  print ( 'problem5():' )
  print ( '  Heron\'s triangle area formula.' )
  
  a = 10
  b = 12
  c = 6
  s = ( a + b + c ) / 2.0
  area = sqrt ( a * ( s - a ) * ( s - b ) * ( s - c ) )
  print ( '  Area = ', area )

  print ( '' )
  a = 5
  b = 12
  c = 6
  s = ( a + b + c ) / 2.0
  try:
    area = sqrt ( a * ( s - a ) * ( s - b ) * ( s - c ) )
    print ( '  Area = ', area )
  except ( ValueError ):
    print ( '  Illegal square root!' )
  
  return

def problem6 ( ):

#*****************************************************************************80
#
## problem6(): Dice problem.
#
  from math import sqrt
  
  print ( '' )
  print ( 'problem6():' )
  print ( '  The dice problem.' )
 
  a = 2
  b = 6
  c = ( ( 3 * ( a**3 * b - b**3 * a ) ) % 7 )
  print ( '  a = ', a, '  b = ', b, '  c = ', c )
  
  a = 3
  b = 5
  c = ( ( 3 * ( a**3 * b - b**3 * a ) ) % 7 )
  print ( '  a = ', a, '  b = ', b, '  c = ', c )
  
  return
  
def problem7 ( ):

#*****************************************************************************80
#
## problem7(): Paper folding
#
  from math import log
  
  print ( '' )
  print ( 'problem7():' )
  print ( '  Repeatedly fold a piece of paper.' )
 
  tmm = 0.1
  Dkm = 384400
  k = log ( Dkm * 1000000 / tmm ) / log ( 2 )
  k = int ( k + 1 )
  print ( '  k = ', k )
  
  return
  
def problem8 ( ):

#*****************************************************************************80
#
## problem8(): Earth surface area
#
  from math import atanh
  from math import pi
  from math import sqrt
  
  print ( '' )
  print ( 'problem8():' )
  print ( '  Earth surface area.' )
 
  a = 6378137.0
  c = 6356752.314245
  e = sqrt ( 1 - c**2 / a**2 )
  area = 2.0 * pi * a**2 * ( 1 + ( 1 - e**2 ) / e * atanh ( e ) )
  print ( '  Estimate for Earth surface area = ', area )
  
  return

def problem9 ( ):

#*****************************************************************************80
#
## problem9(): Estimate exp(4)
#
  from math import exp
  from math import factorial
  
  print ( '' )
  print ( 'problem9():' )
  print ( '  Estimate exp(4).' )
  
  exact = exp ( 4.0 )
  print ( '  Exact value of exp(4) = ', exact )
  
  est = 0
  k = -1
  x = 4.0
  
  k = k + 1
  est = est + x**k / factorial ( k )
  print ( '  Estimate ', k, ' = ', est, '  error = ', abs ( est - exact ) )

  k = k + 1
  est = est + x**k / factorial ( k )
  print ( '  Estimate ', k, ' = ', est, '  error = ', abs ( est - exact ) )

  k = k + 1
  est = est + x**k / factorial ( k )
  print ( '  Estimate ', k, ' = ', est, '  error = ', abs ( est - exact ) )
  
  k = k + 1
  est = est + x**k / factorial ( k )
  print ( '  Estimate ', k, ' = ', est, '  error = ', abs ( est - exact ) )
  
  k = k + 1
  est = est + x**k / factorial ( k )
  print ( '  Estimate ', k, ' = ', est, '  error = ', abs ( est - exact ) )

  k = k + 1
  est = est + x**k / factorial ( k )
  print ( '  Estimate ', k, ' = ', est, '  error = ', abs ( est - exact ) )

  k = k + 1
  est = est + x**k / factorial ( k )
  print ( '  Estimate ', k, ' = ', est, '  error = ', abs ( est - exact ) )

  k = k + 1
  est = est + x**k / factorial ( k )
  print ( '  Estimate ', k, ' = ', est, '  error = ', abs ( est - exact ) )
  
  k = k + 1
  est = est + x**k / factorial ( k )
  print ( '  Estimate ', k, ' = ', est, '  error = ', abs ( est - exact ) )
  
  k = k + 1
  est = est + x**k / factorial ( k )
  print ( '  Estimate ', k, ' = ', est, '  error = ', abs ( est - exact ) )
  
  return
  
if ( __name__ == "__main__" ):
  problem0 ( )
  problem1 ( )
  problem2 ( )
  problem3 ( )
  problem4 ( )
  problem5 ( )
  problem6 ( )
  problem7 ( )
  problem8 ( )
  problem9 ( )