area of a figure is fixed , then how can it have irrational value.
eg: area of a cirle or radius 2 units is fixed , but when calculated its value works out to be pi*(2^2) - which is irrational. how??
2006-09-21 04:40:29 · 11 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
irrational has nothing to do with an area being fixed. irrational numbers are numbers just like anything else. If a value of something is sqrt(2)/2 it is irrational, but it is still a real value.
2006-09-21 04:48:48 · answer #1 · answered by nurseme0w 2 · 0⤊ 0⤋
In math, the term irrational just refers to a number that cannot be expressed as a ratio of two integers. The most common irrational numbers are square roots, but there are many others. An area of a rectangle measuring 1 by squareroot(2) is irrational. There is nothing unusual about an area being irrational. This can happen when one of the contributing dimensions is irrational. The area of a circle is typically irrational because it involves pi and pi is irrational.
For what its worth, pi is irrational but it is one step beyond that. It is a transcendental number meaning that it cannot be expressed in terms of rational numbers or roots of rational numbers so your area is transcendental as well as irrational.
2006-09-21 04:52:19 · answer #2 · answered by Pretzels 5 · 1⤊ 0⤋
Technically, the value is fixed, pi*2^2 is definitely a fixed value
However, the value of pi is not known as it is irrational. This is because geometrically it is not possible to find the area of a circle or circumference perfectly.
So, whenever you find the area or circumference of a circle mathematically, you never get the actual value!!!
2006-09-21 05:43:36 · answer #3 · answered by Anand 2 · 0⤊ 0⤋
For another example of this phenomenon, try
finding the area of an equilateral triangle with
integral side. You will find that the answer
involves sqrt(3), which is irrational!
2006-09-21 04:59:07 · answer #4 · answered by steiner1745 7 · 0⤊ 0⤋
irrational means that it cannot be defined at all level of accuracy. The exact value of pi can only be defined with infinite accuracy but that doesn't mean that it hasn't an exact value. Indeed, it has but we cannot know it.
2006-09-21 05:22:20 · answer #5 · answered by goncuf 1 · 0⤊ 0⤋
i think its because the creator of pi hasnt finalised the final version as it keeps going on forever(well it seems that way) but eventually we might get a rational pi number, which is still being worked out by computers. therefore until we get a rational pi the answer u work out will be irrational.
2006-09-21 04:45:08 · answer #6 · answered by Anonymous · 0⤊ 2⤋
Hi. Pi times 4 is a perfectly rational number.
2006-09-21 04:42:09 · answer #7 · answered by Cirric 7 · 0⤊ 2⤋
When the area of the fixed figure is concave negative.
2006-09-21 04:42:19 · answer #8 · answered by The Ultimate Answerer 3 · 0⤊ 2⤋
dont know
2006-09-21 04:41:51 · answer #9 · answered by roc a wear 2 · 0⤊ 2⤋
i suck at math sorry!
2006-09-21 04:41:45 · answer #10 · answered by Anonymous · 0⤊ 3⤋