2006-08-01 04:19:49 · 13 answers · asked by Pratham daga 1 in Science & Mathematics ➔ Mathematics
pi can be expressed as the ratio of circumference by diameter .both the values are rational that means pi is expressed in the form of m/n . which means it should be rational.
2006-08-01 04:30:10 · update #1
The diameter and circumference are never both rational; at the most one is rational. Often times the value for the diameter or circumference are rounded, just as pi is often rounded to 3.14, which is why they appear rational.
Pi was proven to be irrational in the 18th century by Johann Lambert, but the proof is somewhat complicated.
You can get an idea of how it is irrational by superimposing a polygon over a circle (square, pentagon, hexagon, etc.) and calculating its area, then increasing the number of sides and doing the same.
2006-08-01 04:38:15 · answer #1 · answered by Fudge 2 · 5⤊ 3⤋
Pi is irrational because it cannot be expressed as a fraction where the numerator and denominator are integers.
The circumference and the diameter of the same circle cannot both be rational.
So when you calculate e.g. the circumference of a circle, if you leave the answer as some constant multiplied by Pi it is more accurate than if you try to evaluate Pi.
Pi can be expressed as an infinite power series i.e.
4 x summation n from 1 to infinity ((-1)^n+1)/(2n-1)
2006-08-01 11:38:00 · answer #2 · answered by Anonymous · 0⤊ 1⤋
Pi is irrational because it cannot be expressed as a ratio of integers. Even if you have an exact diameter as an integer, the circumference will not also be an integer ever. If you have an exact integer for the circumference then the diameter will not be an integer ever.
Referring to your additional details, BOTH CAN"T EVER BE RATIONAL!!
2006-08-01 11:23:44 · answer #3 · answered by MollyMAM 6 · 0⤊ 1⤋
Right. It is not possible for both the diameter and the circumference of a circle to be rational. One or the other can be, but not both at the same time.
2006-08-01 12:08:08 · answer #4 · answered by mathematician 7 · 0⤊ 1⤋
Good question. So, if the relationship between circumference and diameter can never be rational, maybe we should explore new ways of thinking about circles..
2006-08-01 19:45:34 · answer #5 · answered by Anonymous · 0⤊ 0⤋
so could Pi expressed in a different number base be a rational number? eg. base 12 or base 8?
2006-08-01 11:49:16 · answer #6 · answered by Anonymous · 0⤊ 0⤋
Irrational Numbers are numbers that cannot be expressed as fractions. The decimal expansion of an irrational number neither terminates or repeats. Therefore, irrational numbers include all non-perfect roots, all non-terminating, non-repeating decimals and =3.1415....
2006-08-01 11:25:04 · answer #7 · answered by DanE 7 · 0⤊ 1⤋
An irrational number is one which can never be expressed exactly by dividing one integer by another.
2006-08-01 11:24:13 · answer #8 · answered by Owlwings 7 · 0⤊ 1⤋
it means that
1) if radius is rational, then diameter is irrational
2) if diameter is rational, then radius is irrational
3 if raidus or diameter is irrational, then you cannot say if the other one is rational or irrational.
2006-08-01 11:38:44 · answer #9 · answered by Anonymous · 0⤊ 1⤋
Yes
2006-08-01 11:25:10 · answer #10 · answered by ag_iitkgp 7 · 0⤊ 1⤋