Chris Van Schyndel Dev-Sprint2

chap6.py

@@ -1,9 +1,54 @@
-# Enter your answrs for chapter 6 here
-# Name:
+# Enter your answers for chapter 6 here
+# Name: Christopher Van Schyndel
 
 
 # Ex. 6.6
 
+def first(word):
+	return word[0]
+
+def last(word):
+	return word[-1]
+
+def middle(word):
+	return word[1:-1]
+
+# 1a. Returns an empty string ( no space ), as there is nothing in the middle of a two letter string.
+# 1b. Also returns an empty string ( no space ), as you are indexing nothing.
+
+# 2.
+
+# This function takes a string and returns True if it is a Palindrome, and False otherwise.
+def is_palindrome(string):
+	pass
+	length = (len(string) / 2)
+	stringchecker1 = ''
+	stringchecker2 = ''
+	for length in range(length):
+		stringchecker1 += string[length]
+		stringchecker2 += string[-(length+1)]
+	if stringchecker1 == stringchecker2:
+		return True
+	else:
+		return False
+
+# Ex 6.8
+
+# This function finds the greatest common denominator of two integers.
+# It should, but will not work for decimals in python.  It is likely that the decimal
+# module is required to fix this.  Ex. 1.0 % 0.2 gives the result 0.2.  However, 1.6 % 0.2
+# gives the result 0.
+def gcd(a, b):
+	if a != 0 and b != 0:
+		r = a % b
+		print r
+		print str(b)
+		if r != 0:
+			gcd(b, r)
+		else:
+			print "The greatest common denominator is " + str(abs(b))
+	else:
+		print "Cannot find the gcd of 0!"
+
 
 
-# Ex 6.8

chap7.py

@@ -1,9 +1,29 @@
-# Enter your answrs for chapter 7 here
-# Name:
-
+# Enter your answers for chapter 7 here
+# Name: Christopher Van Schyndel
 
+import math
 # Ex. 7.5
 
+def estimate_pi():
+	left = 2* math.sqrt(2) / 9801.0
+	k = 0
+	estimate = 0
+	# summation infinity -> k = 0
+	while True:
+		numerator = math.factorial(4*k) * (1103 + 26390*k) 
+		denominator = math.factorial(k)**4 * 396 ** (4*k)
+		# Overflow error unless calculations are seperated out.
+		# step = left * math.factorial(4*k) * (1103 + 26390*k)  / math.factorial(k)**4 * 396 ** (4*k)
+		step = left * numerator / denominator
+		estimate += step
+		k += 1
+		if step < 1e-15: 
+			break
+	print k
+	return 1 / estimate
+
 
+# How many iterations does it take to converge?
 
-# How many iterations does it take to converge?
+print estimate_pi() == math.pi
+# It takes 3.