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why is PI considered irrational if it can be expressed as ratio of circumference to diameter? [duplicate]

Pi = C / D (circumference / diameter) . I have read that if circumference can be expressed as an integer then diameter cannot and vice-versa, so that the ratio can never be expressed as a/b where both ...
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6k views

Why can't $\pi$ be expressed as a fraction? [duplicate]

Why can't $\pi$ be expressed as a fraction? If pi is the ratio of a circle's circumference to its diameter, why can't we simply take a circle, measure its circumference and diameter, and derive the ...
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554 views

how $\pi$ is irrational if it is a ratio [duplicate]

How can $\pi$ be an irrational number if it is a ratio of the circumference over the diameter? Thanks!
907 views

Irrationality of $\pi$ and circumference to diameter ratio. [duplicate]

How is $\pi$ actually defined? If it is defined as the ratio of the circumference of a circle to its diameter then from this definition itself either of the circumference and diameter has to be ...
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135 views

Why is PI considered irrational if it is already defined as ratio of circumference to diameter? [duplicate]

Why is PI considered irrational if it is defined as ratio of circumference to diameter? And how do we close the value of circumference and diameter to a certain number without giving up accuracy at ...
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The irrationality of Pi [duplicate]

Pi is defined as circumference/diameter, but it is an irrational number. And by definition an irrational number can't be defined by a fraction. So how is it that pi is circumference/diameter and on a ...
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82 views

Why PI is an irrational number? [duplicate]

Since my understanding of rational number says that it can expressed as fraction of 2 integers. $Q = \frac{p}{q}$ where, $p,q$ belongs I What I don't understand is how does PI fail to qualify these ...
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50 views

$π = \frac{c}{d}$ [duplicate]

We know that $π = \frac{c}{d}$, where $c$ is circumference of circle and $d$ is diameter of circle. I surprised to see $π = \frac{c}{d}$ where $π$ is an irrational number and $\frac{c}{d}$ is rational ...
I tried to find what makes a number $\pi$ special. $22/7$, $355/113 \approx\pi$, which is an irrational number. Why is this constant is used for defining any cyclic function? Why is it that this ...