Pie-the Infinite Number
Introduction
The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes written as "pi. π is an irrational number, which means that it cannot be expressed exactly as a ratio of any two integers (fractions such as 22/7 are commonly used to approximate π; no fraction can be its exact value); consequently, its decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be randomly distributed, although no proof of this has yet been discovered. π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge.
In the 20th and 21st centuries, mathematicians and computer scientists discovered new approaches that – when combined with increasing computational power – extended the decimal representation of π to, as of late 2011, over 10 trillion (1013) digits. [1] Scientific applications generally require no more than 40 digits of π, so the primary motivation for these computations is the human desire to break records, but the extensive calculations involved have been used to test supercomputers and high-precision multiplication algorithms.
Relationship of pi with circle The circumference of a circle relates to one of the most fundamental and important mathematical constants in all of mathematics. This constant p , is represented by the Greek letter π. The numerical value of π is 3.14159 26535 89793 ...., and is defined by two proportionality constants. The first constant is the ratio of a circle's circumference to its diameter and equals π. While the second constant is the ratio of the diameter and two times the radius and is used as to convert the
The number π is a mathematical constant that is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes written as "pi. π is an irrational number, which means that it cannot be expressed exactly as a ratio of any two integers (fractions such as 22/7 are commonly used to approximate π; no fraction can be its exact value); consequently, its decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be randomly distributed, although no proof of this has yet been discovered. π is a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge.
In the 20th and 21st centuries, mathematicians and computer scientists discovered new approaches that – when combined with increasing computational power – extended the decimal representation of π to, as of late 2011, over 10 trillion (1013) digits. [1] Scientific applications generally require no more than 40 digits of π, so the primary motivation for these computations is the human desire to break records, but the extensive calculations involved have been used to test supercomputers and high-precision multiplication algorithms.
Relationship of pi with circle The circumference of a circle relates to one of the most fundamental and important mathematical constants in all of mathematics. This constant p , is represented by the Greek letter π. The numerical value of π is 3.14159 26535 89793 ...., and is defined by two proportionality constants. The first constant is the ratio of a circle's circumference to its diameter and equals π. While the second constant is the ratio of the diameter and two times the radius and is used as to convert the