Teachers state that the circumference of a circle is 2*pi*r. However, pi is irrational, so therefore so is the circumference of a circle, so can we ever know the circumference of a circle?
2006-09-18 09:13:17 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
This isn't a question of accuracy, but of the fact that the circumference of a circle is an irrational number but never expressed as such and is often considered to be rational.
2006-09-18 09:29:57 · update #1
If you don't believe me, ask your maths' teacher if the circumference of a circle is an irrational number and see what they answer (it obviously is).
2006-09-18 09:31:13 · update #2
If you think pi isn't an irrational number, jooker and joecseko, why are you attempting to answer maths questions?
Suggest you go here and be educated just a little:
http://en.wikipedia.org/wiki/Irrational_number
http://en.wikipedia.org/wiki/Pi
2006-09-23 08:31:56 · update #3
Yes pi is irrational. In fact, it is called transcendental
because it is not the solution of any algebraic polynomial
equation with rational coefficients.
So the circumference C of a circle with a rational radius R is
indeed C = 2*pi*r and is irrational.
However, pi can be computed to any number of digits,
i.e. to any accuracy. Hence if we know the radius, we
can compute the circumference to any degree of accuracy.
This is what we mean by measurement.
2006-09-23 12:04:32 · answer #1 · answered by David Y 5 · 1⤊ 0⤋
Take any circle in the plane. enable C be the circumference of the circle. enable D be the diameter of the circle. no rely what circle you %., C / D is often the comparable. %. 3 or 5 or a million circles, the C/D of one circle is exactly equivalent to the C/D of yet another. it is incredibly astounding, and it is not in any respect glaring why it would be real, even yet it is: the ratio of a circle's circumference to a diameter is a relentless value, and pi is what mathematicians have desperate to call this consistent value.
2016-12-12 10:42:06 · answer #2 · answered by ? 4 · 0⤊ 0⤋
Well, when it comes to calculations using an irrational number we have to make up our mind as to how accurate an answer we need.
So u must determine how much accuracy u need when u calculate the circumference. And we know the value of 'Pi' up to millions of digits. So u actually have more than enough accuracy for any ordinary routine applications. Its enough even for high precision Astronomical uses.
Having said that, since 'Pi' is Circumfrerence divided by Diameter, it must essentially remain irrational. Else it would mean that 'Pi' would be rational.
2006-09-18 09:16:20 · answer #3 · answered by Maverick 2 · 1⤊ 2⤋
You'll only get approximations when you measure something. If you measure the radius and circumference of a circle, both will (most likely) be rational approximations.
But, if you measure the radius and circumference as closely as possible-- and if you take the average of lots of measurements-- you'll get closer and closer to the 2*pi* formula.
2006-09-18 09:20:23 · answer #4 · answered by btsmith_y 3 · 0⤊ 2⤋
Depends on the accuracy you require.
You could use a tape measure, but you'll be limited by the thickness of the markings, and if you had a quantom measuring device, you'ld still be limited by planks constant.
2006-09-18 09:16:30 · answer #5 · answered by Master J 4 · 1⤊ 2⤋
after you pass the 2nd or 3rd decimal of pi, the decimals numbers will be so small that they won't even make any difference in your measurements.
2006-09-18 09:29:38 · answer #6 · answered by Sergio__ 7 · 1⤊ 2⤋
I don't know if that answer will fly with the teacher. But the best of luck to you.
2006-09-18 09:21:13 · answer #7 · answered by dmgoldsbo7 3 · 1⤊ 2⤋
pi isn't irrational, dude, you may be however....
2006-09-18 09:21:11 · answer #8 · answered by jooker 4 · 3⤊ 1⤋