9.8  Jeff ASagarin WED. 
  
 9. REVIE QUESTIONS.123-136 including evens, CLT: 104, 105, 106.    No calculators.
 


https://en.wikipedia.org/wiki/Square_root_of_2 CONSTRUCTIVE PROOF. 

###############################################
 #program squareroot
#    2022 April 18 Monday

print("What number do you want the square root of?")
number = int(input()) #This asks for the user to input a number on the screen, 
#and makes it an integer type, not a string.
print("\n")

print("What is your initial guess as to the square root of",number,"?")
guess = int(input())
print("\n")

print("How many iterations do you want this estimate to run for")
number_of_iterations = int(input())
print("\n")
 
print("You have chosen the number to square rooted to be", number, ", the \
initial guess to be", guess, ", and the number of iterations to be", number_of_iterations, ".\n") 

estimate = guess
iteration = 0

for item in range(number_of_iterations):
  iteration = iteration+1
  last_estimate = estimate 
  estimate = .5*(last_estimate + number/last_estimate)
  print("On iteration", iteration,   "the last estimate of sqrt(",number, ") was", \
         last_estimate, ", and the new estimate is ", estimate,".\n")
  
          

"""
program squareroot
!     2022 April 18 Monday
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
1     write(6,*) 'enter number to find square root of, initial guess,',
     & ' iterations'
      read(5,*,end=30) z,x00,numitr
      x=x00
      y=x00
      iter=0
      write(6,*) 'number            initial guess     estimate',
     & '          actual            iteration'
10    iter=iter + 1
      if(iter.gt.numitr) goto 20
      y=z/x
      x0=x
      x=0.5d0*(x + y)
      write(6,*) z,x0,x,dsqrt(z),iter
      goto 10
20    write(6,*) z,x0,x,dsqrt(z)
      goto 1
30    stop
      end
      """
  
 
https://www.mathsisfun.com/numbers/euclid-square-root-2-irrational.html

  

https://twitter.com/LongFormMath/status/1511100395925368836 Pythaogrean THeorem proof. 

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