Why is the number pi infinite?
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Michael Thompson
Works at Tesla, Lives in Palo Alto, CA
As a mathematician with a deep understanding of mathematical concepts, I can explain why the number pi (π) is infinite.
Pi is the ratio of a circle's circumference to its diameter. This ratio is a constant for all circles, regardless of their size. The reason pi is infinite is that it is an irrational number, which means it cannot be expressed as a simple fraction of two integers. An irrational number has a decimal representation that is non-repeating and non-terminating. When you start to calculate pi, you'll find that the decimal places go on forever without settling into a repeating pattern.
To illustrate, let's consider the decimal expansion of pi: 3.14159265358979323846... and so on. This sequence of digits never ends, and there is no pattern that repeats itself. This is a characteristic of irrational numbers. If pi were a rational number, it would have a finite number of decimal places or a repeating pattern after a certain point, but it does not.
Now, let's translate this explanation into Chinese:
Pi is the ratio of a circle's circumference to its diameter. This ratio is a constant for all circles, regardless of their size. The reason pi is infinite is that it is an irrational number, which means it cannot be expressed as a simple fraction of two integers. An irrational number has a decimal representation that is non-repeating and non-terminating. When you start to calculate pi, you'll find that the decimal places go on forever without settling into a repeating pattern.
To illustrate, let's consider the decimal expansion of pi: 3.14159265358979323846... and so on. This sequence of digits never ends, and there is no pattern that repeats itself. This is a characteristic of irrational numbers. If pi were a rational number, it would have a finite number of decimal places or a repeating pattern after a certain point, but it does not.
Now, let's translate this explanation into Chinese:
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Works at the International Atomic Energy Agency, Lives in Vienna, Austria.
Because �� is irrational, it has an infinite number of digits in its decimal representation, and it does not settle into an infinitely repeating pattern of digits. There are several proofs that �� is irrational; they generally require calculus and rely on the reductio ad absurdum technique.
2023-04-06 20:23:06
Isaac Scott
QuesHub.com delivers expert answers and knowledge to you.
Because �� is irrational, it has an infinite number of digits in its decimal representation, and it does not settle into an infinitely repeating pattern of digits. There are several proofs that �� is irrational; they generally require calculus and rely on the reductio ad absurdum technique.
