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Line 1: − + − The value of <big><math>\pi</math></big> is an [[irrational number]]; which means that it cannot be fully expressed as a fraction or a decimal (regardless of the number of digits used). + − − − − − +
Assorted changes.
'''Pi''' (<big><math>\pi</math></big>) is the ratio of the circumference of a circle to its diameter: approximately 3.14159 (but mathematicians have struggled for centuries to provide better and better approximations). Using the convention that Greek letters in mathematics have conventional meaning, the ratio takes its name from the sixteenth letter of the [[Greek alphabet]]. It is an important number and appears in many [[mathematical]] and [[physics|physical]] formulae.
'''Pi''' (<big><math>\pi</math></big>) is the ratio of the circumference of a circle to its diameter. The value of <big><math>\pi</math></big> is an [[irrational number]]; which means that it cannot be fully expressed as a fraction or a decimal (regardless of the number of digits used). To five decimal places, <big><math>\pi</math></big> <big><math>\approx</math></big> 3.14159. Using the convention that Greek letters in mathematics have conventional meaning, the ratio takes its name from the sixteenth letter of the [[Greek alphabet]]. It is an important number and appears in many [[mathematical]] and [[physics|physical]] formulae.
The approximate value of 3.14159 is precise enough for almost all ordinary purposes; it can, for example, be used to calculate the circumference of a circle of the size of the Earth with an error of only about 110 feet. For rough approximations, the fraction 22/7 (= 3.142857...) is sometimes used.
The approximate value of 3.14159 is precise enough for almost all ordinary purposes; it can, for example, be used to calculate the circumference of a circle of the size of the Earth with an error of only about 110 feet.
For rough purposes, the fraction 22/7 (= 3.142857...) is sometimes used.
==History==
==History==
To some extent, the progress of mathematics—or at least of computation—can be gauged by the progress in the number of digits to which <big><math>\pi</math></big> has been calculated.
Mathematicians have worked for centuries to calculate <big><math>\pi</math></big> to more and more decimal places. To some extent, the progress of mathematics—or at least of computation—can be gauged by the progress in the number of digits to which <big><math>\pi</math></big> has been calculated.
Some ancients expressed <big><math>\pi</math></big> by using fractional approximations. Papyrus of Ahmes, dated c. 1650 B.C., shows that ancient Egyptians had value 3 1/6 = 3.167). The Babylonian value from the same era was 3 1/8 = 3.125<ref>Boyer, A History of Mathematics, 2nd Edition</ref>. Both these values are accurate to within 1 percent. Note that the value 22/7 (3 1/7) is still used today.
Some ancients expressed <big><math>\pi</math></big> by using fractional approximations. Papyrus of Ahmes, dated c. 1650 B.C., shows that ancient Egyptians had value 3 1/6 = 3.167). The Babylonian value from the same era was 3 1/8 = 3.125<ref>Boyer, A History of Mathematics, 2nd Edition</ref>. Both these values are accurate to within 1 percent. Note that the value 22/7 (3 1/7) is still used today.