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talljasperman's avatar

Why do teachers say that Pi is infinite?

Asked by talljasperman (21875points) October 20th, 2011

If a solid circular object exists in reality then it must end specifically. The distance can’t be less than one atom without becoming absurd (right)? Also how is Pi calculated? I was taught that you just get 22 divided by 7 to get Pi… isn’t it weird that you can get a specific number for is universal constant only when you have exactly 22 divided by 7.

Topics: Math, Pi,

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29 Answers

robmandu's avatar

22 ÷ 7 ≠ π. It’s an approximation just to get you the first few digits in case your calculator doesn’t have a π button.

robmandu's avatar

π = 3.1415926535897932384626433832795…

22 ÷ 7 = 3.1428571428571428571428571428571

talljasperman's avatar

@robmandu How did they come up with π = 3.1415926535897932384626433832795…How did the mathematicians find that out…? They couldn’t of just measured a circle with a measuring tape that accurately ?... They must have used a calculation?

robmandu's avatar

Wikipedia explains:

π is an irrational number, which means that its value cannot be expressed exactly as a fraction having integers in both the numerator and denominator. Consequently, its decimal representation never ends or repeats. π is also a transcendental number, which implies, among other things, that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can render its value; proving this fact was a significant mathematical achievement of the 19th century.

- and -

The next major advances in the study of π came with the development of infinite series and subsequently with the discovery of calculus, which permit the estimation of π to any desired accuracy by considering sufficiently many terms of a relevant series.

talljasperman's avatar

@robmandu So π is not an accurate… number… so what do engineers use when building circles? Sounds like only the university students get the real useful education and the high school students get lab accidents when using π in the real world….Maybe π is wrong or has little correlation when used practically. π is starting to sound like that remainder or leftovers when dividing longhand…completely useless without having a better more accurate and profound grasp of math. How deep into math does one have to go before it is accurate and precise enough to use in the real world?

robmandu's avatar

Great questions so far.

Everybody that makes decent circles uses π... all the way back to the ancient Egyptians and on into the far-distant future.

The precision of π isn’t in doubt… and the engineering task at hand determines the level of accuracy (number of digits) needed.

Just because something can’t be described to a finite number of decimal places doesn’t mean it isn’t useful or valid.

robmandu's avatar

How Stuff Works has a really helpful illustration and explanation of π.

shrubbery's avatar

To be honest I’m doing engineering right now and it’s kind of an inside joke but also kind of true that engineers just round off to make things easier like we would assume a horse is a sphere just to make our calculations easier and we could approximate Pi to 3 just as long as at the end you increase by a safety factor to cover your rounding errors.

robmandu's avatar

@shrubbery, you mean like this, right?

talljasperman's avatar

@robmandu

From the article How stuff works:

There are ways to calculate pi that have nothing to do with circles. Using these techniques, pi has been calculated out to millions of digits.
Check out the next page for more information about calculating pi and different things that you can do with it.

I go to the next page and I don’t see the info on calculating pi without circles…is it one of the links below?

LuckyGuy's avatar

@talljasperman What is the decimal equviaent of 10/3? 3.3? 3.33? 3.333333333…... Pi is the same way.

Here are a couple of ways to calculate it
Vieta’s Formula
2/PI = sqrt2/2 * sqrt( 2 + sqrt2 )/2 * sqrt(2 + ( sqrt( 2 + sqrt2) ) )/2 * ...c

Leibnitz’s Formula
PI/4 = 1/1 – ⅓ + 1/5 – 1/7 + ...

Wallis Product
PI/2 = 2/1 * ⅔ * 4/3 * 4/5 * 6/5 * 6/7 * ...
2/PI = (1 – ½2)(1 – ¼2)(1 – 1/62)...
There are many other ways. If you do a quick search on how to calculate PI you will see them.
22/7 is close enough for most things and it is easy to do in your head.

flutherother's avatar

The first ten trillion digits of pi have now been calculated Someone has also found a way of calculating any arbitrary digit of pi without calculating the preceding ones which was thought impossible until recently

robmandu's avatar

@talljasperman, as @worriedguy mentions, and as my original Wikipedia reference explains, the development of infinite series and calculus maths have together provided techniques by which we can estimate π to as many digits as we want (and have the time to wait for the computations to complete).

The thing is, all of these techniques exist for us to better understand the ratio between a circle’s diameter and circumference.

LostInParadise's avatar

There are two points to make. Firstly, as an irrational number, pi goes forever without repetition. Secondly, there are no perfect circles in the real world. Ultimately, things are made of subatomic particles that are in constant motion. I doubt that any physical significance can be given to more than the first 10 digits of pi and certainly not to any more than the fist 100 digits.

talljasperman's avatar

@robmandu How does a human eye perceive the infinite? The value of Pi must terminate in the human mind subconsciously? Or else we would all go insane when we look at a circle… I wonder how many significant digits the human brain can calculate to in order to perceive the universe in some meaningful way?

robmandu's avatar

I recommend reading some Douglas Adams for answers to some of these psycho-philosophical questions. Adams explains that “infinity is boring”. Indeed, we experience infinity every time we look up into the night sky.

talljasperman's avatar

@robmandu I have Hitchhikers Guide to the Galaxy in my bookshelf… I will read it. I’ve watched both movies and I liked them…

prasad's avatar

You may read following books if it interests you.
History of Pi by Petr Beckmann
e: The Story of a Number by Eli Maor

And, you can take a look at Supplementary Reading references given on this site.

Mariah's avatar

“If a solid circular object exists in reality then it must end specifically. The distance can’t be less than one atom without becoming absurd (right)?”

Yes, only theoretical circles have circumferences of exactly 2πr. In real life, there a smallest possible discernable distance called the Plank length. So the closest you can come to a circle in real life is actually a shape with an extremely large number of extremely short sides.

El_Cadejo's avatar

@talljasperman both movies? Im only aware of one. Also the movie pales horribly in comparison to the book.

talljasperman's avatar

@uberbatman The 4 VHS tapes with the petunia and the whale free falling to a planet where the petunia says oh no not again; and then the 2 – 3 hour remake in 2004 or so.

El_Cadejo's avatar

@talljasperman are you talking about the old tv show?

talljasperman's avatar

@uberbatman I don’t know I just looked up my movie guides and two were made 1981 and 1985 they are made for t.v. movies… but I rented it from my local video mart 14 years ago… I should have bought it when I had the chance. I liked them better than the remake in 2004.

El_Cadejo's avatar

@talljasperman ahh I’ve always known it as a tv show. Didnt know they were technically movies, it explains why all six episodes flow so smoothly into each other though. I agree though, they are much much better than the 04 movie, also far more true to the books

KateTheGreat's avatar

It’d be awesome to have infinite amounts of pie.

talljasperman's avatar

@KateTheGreat I only know of four places for pie… my fridge, the oven, my mouth, and the store.

flurtherfurther's avatar

Pi is infinite because, if you take Pi and Qi (that which all is made of), or any number and pi creates a circle. There is no real start or end to a circle because circle is made by expanse and expanse is not recognized by darkness (night). You must have something relative to it and once you do, all you have is the Vesica Pices which is light or (day). It is not until it is relative to a trinity that you have plank and still that is very small but very big. The question is which came first the chicken or the egg.

Strauss's avatar

Technically, Pi is not a number, it is a ratio. It is not a value, it is a relationship.

Mariah's avatar

I mean, yes it’s a ratio, but it’s also a number. It is an irrational number that does have a defined value.

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