Welcome, guest | Sign In | My Account | Store | Cart

Pi is a constant, an irrational number and its notation represent the sixteenth letter of the Greek alphabet, though its value is equal to the ratio of a circle’s circumference to its diameter.

However, a Muslim scientist Abu-Abdullah Muhammad Ibn Musa al-Khwarizmi the founder of algebra ( derived from the Arabic word El-Jabr ), arithmetic, and trigonometry, an astronomer, and a geographer C850 studied and proved Pi’s irrationality.(algorithm is derived from his name Khwarizmi ).

I used the circle equation x²+y² = 1 of radius 1 centred at (0,0) and the circle area’s formula to approximate Pi value. y²= 1-x² and y = √(1-x²) is the upper semicircle which will extend from x = -1 to x = 1 and the rectangle method is used to approximate this area of an interval [-1,1].

The area of a circle is A = πr², thus the semicircle of radius 1 will have an area A = ½ π(1²).

Using my Pi_Approximation program allows you to represent Pi to infinity of digits, and this will depend of the project type and the precision needed, though space programs require to approximate pi at its maximum precision.

And my Pi_Approximation program allows you to make a better Pi’s approximation than the scientific Calculators

Python, 153 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153``` ```#On the name of ALLAH and may the blessing and peace of Allah #be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam. #Author : Fouad Teniou #Date : 23/02/10 #version :2.6 """ Pi_approximation uses the subinterval_length function and return its value and yield all the points values while using the subinterval_point function and Pi function compute Pi approximation with 16 decimal places the greater the value of the number the more precise is Pi value """ class Pi_Approximation(object): """ Class that represent Pi approximation """ def __init__(self, number): """ Pi_Approximation constructor takes the number constant """ self.number = number def subinterval_length(self): """ Compute subinterval_length """ sub_length = 2/float(self.number) return sub_length def subinterval_point(self): """ Compute the value of each point """ #attempt to yield all the Xk points values using the subinterval_point try: for item in range(1,self.number + 1): sub_point = -1 + ((item - 1/2.0)* Pi_Approximation.subinterval_length(self)) yield sub_point #Raise TypeError if input is not numerical except TypeError: print "\n Fouad Teniou (author) 13 years, 3 months ago Fouad Teniou (author) 13 years, 2 months ago Fouad Teniou (author) 11 years, 10 months ago

A switch to C# and a new link Created by Fouad Teniou on Wed, 24 Feb 2010 (MIT)