Why does pi an irrational number

First you are right, I have to learn the Math 'Talk' language, unfortunately I am not coming from a maths back ground at all, but I will do my best.

Secondly what I meant by finite measurement is that the circumference of a circle is finite, has an end.

So my Logic suggested seems reasonable logic to me at the moment that if one makes a calculation between a finite number and an irrational number how can that calculated result ever end? I am not trying to be difficult or pedantic, just wondering if there is an explanation for the fact that the Irrational number has to be arbitrarily rounded up to nth decimal places for any equation to make geometric sense.

The alternative is that the answer has no end either? So a circle never ends- the circumference has no end? I'm happy to be shot down here if the question is baseless but I needed to ask. Jan 30, I remember seeing, long ago, a proof of a very interesting theorem: "Given a number, c, if there exists a function, f, such that all of its "iterated anti-derivatives" can be taken to be integer valued at 0 and c, then c is irrational.

It seems that your use of "finite" and "infinite" are not just typos, but revel and important issue that has to be cleared. All real numbers are finite. They are located a finite distance from zero on the number line. In addition to being infinite in length, this sequence can be unbounded in magnitude. But a single number cannot be unbounded. A real number can have finite or infinite decimal expansion.

Note that rational numbers can also have infinite expansion. What separates them from irrational is that expansions of rational numbers are periodic. That's because pi is what mathematicians call an "infinite decimal" — after the decimal point, the digits go on forever and ever. When starting off in math, students are introduced to pi as a value of 3.

These rational expressions are only accurate to a couple of decimal places. While there is no exact value of pi, many mathematicians and math fans are interested in calculating pi to as many digits as possible. The Guinness World Record for reciting the most digits of pi belongs to Rajveer Meenaof India, who recited pi to 70, decimal places while blindfolded in Meanwhile, some computer programmers have calculated the value of pi to more than 22 trillion digits.

The website piday. Add a comment. Active Oldest Votes. So regarding your last question: No! Stefan Perko Stefan Perko I defined, what a number being irrational means. Is it theoretically impossible to measure two arbitrary lengths correctly? Show 2 more comments. Jack M Jack M David K David K Even if we could measure everything with perfect accuracy, we would still find that the circumference is an irrational multiple of the diameter.

The alternative is to use mathematics to determine what C should be, ideally, for some given D, If you start Show 1 more comment. Instead, we need to do a Taylor Series expansion of the inverse tangent. The basic idea behind the Taylor Series is that any function sort of looks like a power series if you just focus on one part of that function. Using this, I can represent the inverse tangent of some value x as an infinite series:.

That's it. Now you can just plug away at this formula for as long as you likeor you could have a computer do it. Here is a program that calculates the first 10, terms in the series just press play to run it :. View Iframe URL. See, that's not so difficult for a computer. However, you can see that even after 10, terms the calculated value is still different than the accepted value.

This isn't the best series to calculate Pibut I said that earlier. This is my favorite Pi activity. Here is the idea. Generate pairs of random numbers between 0 and 1 to create random x,y coordinates. Plot these points on a 1 by 1 grid and calculate their distance to the origin.

Some of these will have a origin distance less than 1 and some will be greater than 1. The points with a distance of less than one are "inside a circle"actually it's a quarter of a circle. You really should play around with this because it's fun. Try changing the number of points or something like that. I included a "rate " statement so you can see the points being added. Oh, run it more than onceeach time you get a different result because of the random part.