Why is PI a never ending number? if you created a circle made out of atoms/quarks before doing the calculation

Question

Wouldn't you be able to get a correct answer?

And for the morons who say there is no beginning to a circle ( 0 degrees ) i would like to know what drugs the are on.

can green_meklar tell me the difference between a theoretical, mathematical circle and one that can be calculated in reality.

Answer 1

pi is an irrational number (i.e., it has an infinite series of non-repeating decimal digits). The first proof was by Johaan Heinrich Lambert in 1761. He proved that if x is rational, tan(x) must be irrational. It follows that if tan(x) is rational, x must be irrational. Since tan(pi/4)=1, pi/4 must be irrational; therefore, pi must be irrational.

Here's an answer for your "construct a circle" scenario (to come up with an "exact" answer for the circumference). Let's go ahead and assume you are able to create a "perfect circle." Whether you use chalk, balsa wood, quarks, etc., the problem that you will encounter is a "measurement" problem. In other words, the limitation in accuracy will be imposed by the measuring instrument.

For example, if you start with a relatively crude instrument, like a tape measure, for a 10" diameter circle, you might measure something like 31.4" for the circumference.

If you do something radical like wrap a wire around it and then very carefully measure the the length of the wire with lasers or something, maybe you'll get 31.4159265" ... The more careful you are, the more significant digits you'll be able to write down in your logbook. If you use quarks, and there are billions of them lined up around the circle (at some rational or "whole number" spacing), at some point, there will either be a slight bit of extra space between two quarks, or one of 'em will be smashed in a little tight. Every time you attempt to realign the quarks, you'll end up with either "irrational spacing" or an odd bit of extra space. OK?

Answer 2

Let's suppose that you create a circle made up of certain particles that are presumably very small. How would this make your calculation more accurate since pi = circumference / diameter. The problem occurs with the quotient. However, suppose your diameter is exactly 1 distance unit, then your circumference would contain n particles whose cumulative length shuold be pi. There would be a problem with your product here too because the distance of each particle will be an irrational number. Get the idea? There is no to obtain an exact representation for pi in any radix system.

Answer 3

Making the circle out of quarks doesn't help. It is quite easy to construct a circle which has a circumference which is an exact (i.e. rational, or even integer) measurement but then the diameter will not be a rational number.
OTOH, if you use an exact number for the diameter, then the circumference will be irrational.

Also, for the responder who said about 22/7
22/7 is an approximation for Pi. Pi itself is irrational - the definition of irrational is that it cannot be expressed as one integer divided by another, so 22/7 is rational, Pi is not.

Answer 4

Pi is based on theoretical, mathematical circles, not actual, physical circles. If you were to do as you suggest, you would reach a rational answer, however your circle would not be perfect. True circles always have an irrational relationship between diameter and circumference.

Answer 5

In a length in quarks yes, but each quark can be divided into fractions as well. The simple answer is that the decimal system isn't completely efficient in calculation, therefore, the expression of certain fractions is a repeating decimal.

Answer 6

Pi is anever ending number because the philosophers in the middle age make a big circle then they create a ratio of the radius and the circumference then the answer was infinitley many numbers.

Answer 7

yes but what u have drawn is technically not a true representation of a circle since it is limited to the number of atoms that is in the ink from which it was drawn.

also just cos the atoms are the smallest particle, the size of the atom could be measured using an infinatly small unit of size (which obviously doesnt exist but technically it could if we wanted).

so isnt it the size we measure and not the number of particles?

Answer 8

22over 7 gives a never ending number, my calculator says 3.1428571, and would go on if the read out was bigger. But how accurate is 22/7, the figures sound to neat to be true.

Answer 9

I would say it is a problem of representation. If your unit for the number system you used was Pi then it would be represented as the nice number 1. Wasn't that what radians were for?

Answer 10

it's a ratio of circumference over radius. The definition of a circle dictates that Pi MUST always be irrational, i.e. never ending. It's a simple case of definition mate.