why does 3.14 never end?

Answer 1

There are some people who will tell you that "that's just how it is. The diameter goes into the circumfrence 3.14159.... times but it never ends". But how do we know this number to thousands of decimal places? Really accurate measuring devices? No. The answer comes with calculus.

If you don't have a grasp of calculus just know that calculus gives us the value of pi. If you know a little something about calc here's the better explanation.

Calculus deals with limits. As this variable approaches this number, what is the limit of the function?

Imagine a circle. I am now going to put four sticks around it and form a square around the circle. I will then measure those sticks. That is my "circumfrence". Obviously it will be quite far off the real value. However, what if we used 8 sticks and made an octagon around the circle? The length of all those sticks would still not be the circumfrence, but it would be closer than when we used 4 sticks. Now how about we use 1000 tiny little sticks and measure all those sticks? The value would be much much closer to the actual circumfrence. Now, theoretically, imagine we use infinity sticks. The measure of those infinity sticks (obviously it's impossible to have this many sticks but that's why this is all done on paper, not in actuality) would be EXACTLY the circumfrence.

In other words, what is the length of all the sticks added together as the number of sticks approaches infinity? The answer is the circumfrence. From this we can derive pi, as long as we know the diameter or radius of our circle.

Some people think egyptians had some knowledge of pi. However, it's unlikely they used calculus to find it out. They probably just used some string and a measuring ruler of some kind to derive pi approximately. They probably said it was a number a little bit larger than 3.

Calculus is the only way you can get the true value of pi. The reason pi is irrational is because it is derived from a limit, not because "it just is". Hopes this helps.

Answer 2

If you mean pi = 3.14, it is an irrational number which a layman interprets as the ratio of the circumference to the diameter of a circle. But it is actually calculated from a Taylor Series expansion of an inverse trigonometric function & since this series is a sum of infinite terms, you cannot predict what is the exact value of the sum (because the terms never stop adding).

tan-1(x) = x - x^3/3 + x^5/5 - x^7/7 + ...

45 degrees = pi/4 radians
&
tan(pi/4) = 1
pi/4 = tan-1(1)

pi/4 = tan-1(1) = 1 - 1^3/3 + 1^5/5 - 1^7/7 + ...

pi = 4*tan-1(1) = 4*{ 1 - 1/3 + 1/5 - 1/7 + ...}

Answer 3

3.14 or pi was coded and written upon during the bible days and has never since ended. The people from those days had long since thought they could bring a end to the equaltion but to this day never have. Some say it is the aftermath of some sort of universal language other claim the number has a ending. I for one have spent countless hours (no pun intended) seeking a finite to this math problem also. Good Luck

Answer 4

ok, any type that terminates or repeats would be written as a fraction. it incredibly is synonymous with being rational. Actuall, the definition of rational is that that is written because of the fact the ratio of two integers. Theorem: The sqrt(2) is irrational. evidence by ability of contradiction: anticipate that sqrt(2) IS rational and as a result would be written as a/b for 2 integers a and b. added, considering the fact that all fractions have a thoroughly decreased variety, we are able to anticipate that a and b are incredibly best. in the past we start, shall we do a lemma. Lemma: If a*a is even, then a could be even. evidence: anticipate a is atypical. Then a*a is atypical. So, a*a is even, if and provided that a is even. Continuation of evidence that sqrt(2) is irrational. a/b = sqrt(2). Squaring the two sides supplies us a*a/(b*b) = 2. a*a = 2*b*b. as a result, a*a is even. So, a could be even. replace a with 2*ok for some ok an integer utilising the definition of even. (2*ok)(2*ok) = 2*b*b. Or, 4*ok = 2*b*b. Mulitply the two sides by ability of a million/2 we get 2*ok = b*b. This tells us that b*b is even. howdy, bear in concepts that lemma that announces if b*b is even that b could be even? So, we end that b is even. we now have arrived at a contridiction because of the fact the two a and b could be even for this to paintings out. yet, wait, a and b are meant to be incredibly best. the only assumption that we made became into that sqrt(2) = a/b. It deliver approximately some thing that became into impossible. this suggests which you are able to not write sqrt(2) as a fraction as a result it is going to by no ability terminate or repeat.

Answer 5

I presume that you are talking about pi. It is a very difficult question - similar to asking why grass is green - it just is. Pi is one of a class of numbers called irrational numbers i.e. ones which are not exactly equal to any fraction and so cannot be expressed as a decimal with any end or repeating pattern. Pi is actually more special than this. It is one of a class of numbers called transcendental numbers (yes, really) which cannot even be expressed using square roots or cube roots etc.

Follow up.
Someone below says that pi has to be irrational because it comes from the limit of an infinite series BUT the limits of infinite series DON'T have to be irrational numbers.

Answer 6

I'll assume you're talking about "Pi", the ratio between a circle's diameter and its circumference.

The reason it never ends actually has to do with the nature of two things: the nature of Pi itself and the nature of the decimal number system.

There's nothing natural about representing numbers decimally. It's a human convenience. We can relate the ten arabic numerals with the ten fingers on our hands and that makes it easy for us to learn how to count when we're young. The decimal system is great for us because we can elegantly write and think about numbers in terms of powers of ten (10, 100, 1000... .01, .001, ...)

But it turns out that Pi doesn't quite fit in with this elegant scheme of powers of ten. There's nothing wrong with Pi, it's just another number. No matter how many digits you write after the "3", you'll always be a teeny tiny bit off, either a wee bit over or a wee bit under the exact value.

Answer 7

Because the relationship between the diameter and circumference is such that it can not end; however, many numbers do not end: consider 1/3, its decimal equivalence goes on forever, and the same for sqrt(2).

Answer 8

Pi is an irrational number, and irrational numbers cannot be expressed as a/b in which a and b are integers. It will never end, and there is no pattern.

Now, why it does that? That's just the way it is, based on how it occurs in nature.

Answer 9

3.14 ends. it's 3 sig figs long.
Just like 21.1 ends and is 3 sig figs long.

Answer 10

It doesnt end just like the circle itself, you can never find all the symmetrical lines on the circle. why?

BECAUSE ITS ALL INFINITE (Never endind)