pi=circumference/diameter so how could it be irrational?

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Bikash Paul

Assistant Professor of Mathematics in Sharda University

Pi=circumference/diameter.But please note that when defining circumference we write 2*pie*r, where r is the radius. What you have written is like one is worshiping Ganges by Ganges.It can be proved that is irrational number which is actually measurement of 180° angel in radians. And definition of rational...
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Pi=circumference/diameter.But please note that when defining circumference we write 2*pie*r, where r is the radius. What you have written is like one is worshiping Ganges by Ganges.It can be proved that is irrational number which is actually measurement of 180° angel in radians. And definition of rational numbers is set of all equivalence classes of the numbers a/b such that a is an integer and b a non zero integers so it is not necessary to have 2*pie*r to be rational. read less
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Tutor

Yes, pi is a irrational.
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Tutor

- Circumference=2*pi*r=pi*D. So pi=C/D. - A rational number is one which can be expressed as a/b, where a is an integer and b is a non-zero integer. - pi is an irrational number has been proved by Lambert and Hermite (refer to their proof...it can be explained here but for lack of using mathematical...
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- Circumference=2*pi*r=pi*D. So pi=C/D. - A rational number is one which can be expressed as a/b, where a is an integer and b is a non-zero integer. - pi is an irrational number has been proved by Lambert and Hermite (refer to their proof...it can be explained here but for lack of using mathematical expressions...you can contact me if you dont understand the proof). So it is obvious that C/D = pi is irrational. Further you may ask that pi=22/7 is a rational number but if you look closely 22/7="3.142.." but pi="3.141592......"is a non-repeating continuous value . Thus 22/7 is a very close approximation of pi but not the actual value of pi. Hence pi=C/D is irrational. read less
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Tutor

A rational number is a ratio of the form a/b where a and b are integers and b is not equal to zero. In the case of pi, the circumference and diameter need not be integers.
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Tutor

pi= P is irrational which which the number is a non-terminating series of numbers approximating the value to desired level of precision. the circumference of a circle is expressed by the following equation: circumference = 2 P r ; here r is the radius of the circle. let me introduce an analogy. recall...
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pi= P is irrational which which the number is a non-terminating series of numbers approximating the value to desired level of precision. the circumference of a circle is expressed by the following equation: circumference = 2 P r ; here r is the radius of the circle. let me introduce an analogy. recall the Bohr model of the atom. the electrons orbit in particular radii. this is quantization-the source of the stability of the atom. this question is trying to introduce the similar situation. the Bohr atom works well explaining the stability of atoms. if P were not to be irrational we would be allowed the construction of some particular circles. this is not the case. we can construct a variety of circles. So there is no problem why P cant be irrational !kindly state the motivation for the question more clearly. read less
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Tutor

It is like dividing 1 by 3. Both 1 and 3 are rational, rather integer. But their division gives a result that is non-ending, i.e. 3333....
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Tutor

Pi is not exactly circumcise/diameter. It is an approximate of that.
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math magician

While getting value of pie, it is 22/7 where 7 i.e., numerator is a non zero numeral proving pi as rational number.
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Trainer

actually it is not a finite terminating value. so it is not rational. so we can say that it is irrational
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Since the value of pi is non-terminating, so its irrational.
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