How is Pi a Ratio if it Cannot be Written as a Fraction?

[cragar]

If pi is the ratio of its circumference to its diameter , But it cannot be written as a fraction
then how is it a ratio ?

 

[Grep]

If pi is the ratio of its circumference to its diameter , But it cannot be written as a fraction then how is it a ratio ?

A ratio doesn't need to be a rational number. A real number is perfectly acceptable.

For example, a ratio could be a ratio between any two numbers, real numbers included. No reason I can't have a ratio of pi/e if I wanted. Still perfectly valid proportions.

 

[cragar]

i see , thanks for your answer , i guess i was thinking of pi as an infinite sum and not a real number.

 

[Jimmy Snyder]

A rational number is not merely a ratio of numbers, it is a ratio of integers.

 

[cragar]

A rational number is not merely a ratio of numbers, it is a ratio of integers.

yes but pi is irrational

 

[Phrak]

If pi is the ratio of its circumference to its diameter , But it cannot be written as a fraction then how is it a ratio ?

Pick a nice circle with unit diameter. Now measure its circumference. The circumference is not in rational units. The fraction is not expressed as two rational numbers.

 

[Jimmy Snyder]

yes but pi is irrational

That means pi cannot be expressed as the ratio of two integers.

 

[billiards]

That means that for all integer value of diameter, there will never be a corresponding integer value of circumference.

 

[Dr Lots-o'watts]

Why does everybody use circumference/diameter and call it pi instead of using diameter/circumference and call it cake (or another Greek letter)?

 

[Curl]

because if the diameter is rational then the circumference isn't, so the ratio is irrational

 

[Char. Limit]

Why does everybody use circumference/diameter and call it pi instead of using diameter/circumference and call it cake (or another Greek letter)?

Mainly because that's just how it happened...

 

[Proton Soup]

Why does everybody use circumference/diameter and call it pi instead of using diameter/circumference and call it cake (or another Greek letter)?

http://en.wikipedia.org/wiki/Pi"

so i guess, convention, getting there first/most often/something. could have just as easily been a chinese symbol for a dragon eating its tail or something.

 

[mugaliens]

Why does everybody use circumference/diameter and call it pi instead of using diameter/circumference and call it cake (or another Greek letter)?

Because the guy pushing the wheel had the final say?

 

[Averagesupernova]

It can be written as a fraction. Just as easily as it can be written as a decimal of 3.1415926... How long do you want to continue carrying the numbers out in either form? Neither one will end.