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Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Circumference of a circle irrational?

The Wavefunction

Area of a circle = pi x r^2
If you have a radius 1 then the area = pi
Therefore the area should be irrational, but surely it's impossible to have an irrational area, it has to be definite.
What am I missing??

Original post by The Wavefunction

Area of a circle = pi x r^2
If you have a radius 1 then the area = pi
Therefore the area should be irrational, but surely it's impossible to have an irrational area, it has to be definite.
What am I missing??

Sorry if I don't understand your question correctly, but an irrational number is still a definite number with a well-defined value, so it's possible for a circle to have an area of 1 units square :smile:

:smile:

there is no reason why the area has to be rational

:boing:

:boing:

The Wavefunction

OP

Original post by NDVA

Sorry if I don't understand your question correctly, but an irrational number is still a definite number with a well-defined value, so it's possible for a circle to have an area of 1 units square :smile:

:smile:

I thought the whole point of irrational numbers was that they were endless, they can't be expressed as a fraction of 2 integers

The Wavefunction

OP

Original post by the bear

there is no reason why the area has to be rational

:boing:

:boing:

Really? That doesn't make sense to me (sorry)

Original post by The Wavefunction

I thought the whole point of irrational numbers was that they were endless, they can't be expressed as a fraction of 2 integers

Yes, irrational numbers can't be expressed as a fraction of 2 real integers, but this has nothing to do with your question :smile:

:smile:

The fact that the decimal representation is infinite has nothing to do with the 'finiteness' of the length. For example, you can have line of length

\frac{1}{3}

, which as a decimal is

0.3333...

, but the line still has finite length :tongue:

:tongue:

(edited 8 years ago)

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