# PI = 3.141 etc? **URL:** \ **Category:** Factual Questions\ **Created:** [May 28, 2000, 9:08pm UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752 "2000-05-28T21:08:13Z")\ **Posts on this page:** 14\ **Page:** 1
**Author:** ![Foggy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/foggy/32/1082_2.png) [@Foggy](https://boards.straightdope.com/u/Foggy)\ **Post date:** [May 28, 2000, 9:08pm UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/1 "2000-05-28T21:08:13Z")
Recently, I read somewhere that someone using computers was able to prove that pi is actually a repeating decimal. I had always been taught that pi was a non-repeating infinite decimal. Because the book I was reading did not reference its source, and only mentioned this factoid in passing, I can’t research it from that end. What is the nature of pi? ---
**Author:** ![Greg\_Charles](https://avatars.discourse-cdn.com/v4/letter/g/839c29/32.png) [@Greg\_Charles](https://boards.straightdope.com/u/Greg_Charles)\ **Post date:** [May 28, 2000, 9:22pm UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/2 "2000-05-28T21:22:48Z")
PI is an irrational number, meaning it is a nonrepeating, nonterminating decimal. I’ve read about several computer programs that have “proved” this fact by carrying out PI to a million places or more. PI can be represented as infinite Taylor series of simple fraction that do follow a pattern, but that’s not the same thing as a repeating decimal. ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [May 28, 2000, 9:24pm UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/3 "2000-05-28T21:24:02Z")
A repeating decimal by its nature is a rational number. Lindemann in 1882 proved that pi is irrational. ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [May 28, 2000, 9:25pm UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/4 "2000-05-28T21:25:34Z")
Pi is irrational. That means it cannot be expressed in terms of a fraction. That means it is an infinite decimal. Furthermore, it means that squaring the circle is impossible(using just a straightedge and a compass to construct a square with the same area as a given circle in a finite amount of steps). Any statements that contradict those facts are either: 1) crackpot (most likely) or 2) groundbreaking (look on CNN, this is bigger than solving Fermat’s Last Theorem). ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [May 28, 2000, 9:28pm UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/5 "2000-05-28T21:28:41Z")
> **[h2g2 - Pi - Edited Entry](https://www.h2g2.com/A211500)** > > Pi, from the edited h2g2, the Unconventional Guide to Life, the Universe and Everything It’s a good site on pi (one of trillions). ---
**Author:** ![bibliophage](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bibliophage/32/7615_2.png) [@bibliophage](https://boards.straightdope.com/u/bibliophage)\ **Post date:** [May 28, 2000, 9:31pm UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/6 "2000-05-28T21:31:46Z")
Correction: That pi is irrational was proved in 1767 by Johaan Heinrich Lambert. A rational number can be expressed as a ratio of integers. That pi is **transcendental** was proved by Lindemann in 1882. A non-transcendental number can be the root of an algebraic equation with rational exponents. The square root of two is irrational but not transcendental. Pi is both irrational and transcendental. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [May 28, 2000, 10:06pm UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/7 "2000-05-28T22:06:23Z")
> [@](#): > > Pi is irrational…Furthermore, it means that squaring the circle is impossible(using just a straightedge and a compass to construct a square with the same area as a given circle in a finite amount of steps). Actually, just the fact that pi is _irrational_ is not quite enough to prove that squaring the circle is impossible. For example, the square root of 2 is irrational, but it is also a constructible number. However, the fact that pi is _transcendental_ is enough to prove that squaring the circle is impossible. ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [May 28, 2000, 10:17pm UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/8 "2000-05-28T22:17:37Z")
Well, it’s still impossible. 🙂 ---
**Author:** ![AWB](https://avatars.discourse-cdn.com/v4/letter/a/bb73d2/32.png) [@AWB](https://boards.straightdope.com/u/AWB)\ **Post date:** [May 29, 2000, 2:05am UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/9 "2000-05-29T02:05:20Z")
Pi is irrational; there’s just no reasoning with it. :D:D ---
**Author:** ![Una\_Persson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/una_persson/32/346_2.png) [@Una\_Persson](https://boards.straightdope.com/u/Una_Persson)\ **Post date:** [May 29, 2000, 3:02am UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/10 "2000-05-29T03:02:18Z")
I had math through PDE’s, and I wish I knew enough to understand how one can prove anumber is irrational, like pi or e. Oh well, I guess that’s why I became an engineer. Any relatively straightforward way to prove that pi or e is irrational to someone who can barely use ordinary DE’s? ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [May 29, 2000, 4:08am UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/11 "2000-05-29T04:08:40Z")
Exceptionally good reference: “A History of Pi” by Petr Beckman. The late Mr. Beckman was testy and let his prejudices bleed through his mathematical history (he hated Aristotle, the Roman Empire, and the Soviet Union, and he let you know it),but he knew his math and what was important. He provides an excellent history of the calculation of Pi. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [May 29, 2000, 6:05am UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/12 "2000-05-29T06:05:39Z")
Quoth Anthracite, > [@](#): > > I wish I knew enough to understand how one can prove anumber is irrational OK, I don’t know how, specifically, you prove that pi is irrational, and I haven’t a clue how you prove something trancendental, but it’s fairly easy to prove that, say, sqrt(2) is irrational. Proof by contradiction: Suppose that sqrt(2) is rational. Then it can be expressed as the quotient of two integers. If these two integers have a common factor, then it can be factored out to produce the “simplest form” of the fraction. In other words, sqrt(2) = a/b , where a and b have no common factors. Rearranging a bit, this means that a[sup]2[/sup] = 2b[sup]2[/sup]. Hence, a[sup]2[/sup] is even, so a is even. Since a and b have no common factors, this means that b must be odd. However, if a is a multiple of 2, then a[sup]2[/sup] must be a multiple of 4. Hence, b = a[sup]2[/sup]/2 must be a multiple of 2. We have, then, that b is both even and odd, a contradiction. Hence, our original assumption that sqrt(2) is rational must be incorrect. ---
**Author:** ![Danielinthewolvesden](https://avatars.discourse-cdn.com/v4/letter/d/ce7236/32.png) [@Danielinthewolvesden](https://boards.straightdope.com/u/Danielinthewolvesden)\ **Post date:** [May 29, 2000, 11:13am UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/13 "2000-05-29T11:13:20Z")
weel, per the Bible, Pi is = to 3, and that is a rational number, right? Is that why wheels don’t roll, also? 😃 ---
**Author:** ![Una\_Persson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/una_persson/32/346_2.png) [@Una\_Persson](https://boards.straightdope.com/u/Una_Persson)\ **Post date:** [May 29, 2000, 2:27pm UTC](https://boards.straightdope.com/t/pi-3-141-etc/20752/14 "2000-05-29T14:27:41Z")
Thanks Chronos, I actually understood that. You’re successfully fighting ignorance!