Why does the number pi never end?
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William Walker
Works at Google, Lives in Mountain View, CA
Hello, I'm a specialist in mathematics, and I'd be happy to explain why the number pi (π) is an infinite decimal.
Pi is the ratio of a circle's circumference to its diameter. It's an irrational number, which means it cannot be expressed as a simple fraction of two integers. The decimal representation of pi goes on forever without repeating, and it contains no discernible pattern. This is because pi is a transcendental number, which is a number that is not algebraic. In other words, pi is not a root of any non-zero polynomial equation with rational coefficients.
The fact that pi is transcendental has been proven through mathematical theorems, most notably by the work of mathematicians such as Johann Lambert, Ferdinand von Lindemann, and Carl Louis Ferdinand von Lindemann, who proved that pi is indeed a transcendental number in the late 19th century.
Pi is the ratio of a circle's circumference to its diameter. It's an irrational number, which means it cannot be expressed as a simple fraction of two integers. The decimal representation of pi goes on forever without repeating, and it contains no discernible pattern. This is because pi is a transcendental number, which is a number that is not algebraic. In other words, pi is not a root of any non-zero polynomial equation with rational coefficients.
The fact that pi is transcendental has been proven through mathematical theorems, most notably by the work of mathematicians such as Johann Lambert, Ferdinand von Lindemann, and Carl Louis Ferdinand von Lindemann, who proved that pi is indeed a transcendental number in the late 19th century.
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Studied at the University of Cape Town, Lives in Cape Town, South Africa.
The digits of pi never repeat because it can be proven that �� is an irrational number and irrational numbers don't repeat forever. If you write out the decimal expansion of any irrational number (not just ��) you'll find that it never repeats. ... That means that �� is irrational, and that means that �� never repeats.
2023-04-12 20:23:06
Mason Hall
QuesHub.com delivers expert answers and knowledge to you.
The digits of pi never repeat because it can be proven that �� is an irrational number and irrational numbers don't repeat forever. If you write out the decimal expansion of any irrational number (not just ��) you'll find that it never repeats. ... That means that �� is irrational, and that means that �� never repeats.
