# should schools stop teaching the 3 4 5 triangle? **URL:** \ **Category:** Great Debates\ **Created:** [November 17, 2009, 4:46am UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886 "2009-11-17T04:46:38Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Attack\_from\_the\_3rd\_dimension](https://avatars.discourse-cdn.com/v4/letter/a/b38774/32.png) [@Attack\_from\_the\_3rd\_dimension](https://boards.straightdope.com/u/Attack_from_the_3rd_dimension)\ **Post date:** [November 17, 2009, 3:34pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/21 "2009-11-17T15:34:14Z")
I just reread the OP, and I think it was written by Doctor Bronner. ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [November 17, 2009, 3:44pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/22 "2009-11-17T15:44:33Z")
The Moral 3-4-5’s? ---
**Author:** ![Chief\_Pedant](https://avatars.discourse-cdn.com/v4/letter/c/a6a055/32.png) [@Chief\_Pedant](https://boards.straightdope.com/u/Chief_Pedant)\ **Post date:** [November 17, 2009, 4:06pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/23 "2009-11-17T16:06:53Z")
Schools should teach simpler concepts at lower levels and more complex concepts at higher levels. Those levels are determined by grade level in general and mental capacity in particular. As a parallel, I might teach a two year old very simple rules about how to speak English correctly. When he is in college he might learn all of those rules are wrong and there are no real “rules.” It was still OK to teach the simple stuff. Remove the bug from your butt about the 3-4-5 being taught in schools. If you want to defend that the concept wrong, go right ahead and explain why. At this point the structure of your OP suggests you are a nutcase rather than someone with an actual concern. If you didn’t mean it that way, please clarify. ---
**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:** [November 17, 2009, 4:13pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/24 "2009-11-17T16:13:57Z")
To the OP: If that amazes you, consider this: 1.) _Every_ odd number is the short side of a right triangle in which the longer side and the hypoteneuse differ by exactly _one_. 2.) If the short side has length 2n + 1, then the longer side has length 2n^2 + 2n (and the hypoteneuse is obviously 2n^2 + 2n +1). n = 1 gives you 3-4-5. n = 2 gives you 5-12-13, and so on. 3.) You can inscribe a circle in each of these triangles, and the radius of the circle will be ---- \*\*n \*\* ! (Not **n!** – I’m expressing surprise, not factorial) 4.) Furthermore, where the inscribed circle touches each side divides that side into integral lengths, as well. By the way, the Egyptians knew about the 3-4-5 right triangle long before Pythagoras. ---
**Author:** ![Keweenaw](https://avatars.discourse-cdn.com/v4/letter/k/da6949/32.png) [@Keweenaw](https://boards.straightdope.com/u/Keweenaw)\ **Post date:** [November 17, 2009, 4:15pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/25 "2009-11-17T16:15:01Z")
> [@msmith537](#): > > the word you are looking for is “[pythagorean](http://en.wikipedia.org/wiki/Pythagorean_theorem)”. > And excuse my ignorance about whatever the hell you are talking about, but does A^2+B^2 no longer equal C^2? Actually I think the word he’s looking for is [Pythagoreanism](http://en.wikipedia.org/wiki/Pythagoreanism) or possibly [Platonic idealism](http://en.wikipedia.org/wiki/Platonic_idealism) Or for fans of Neal Stephenson’s Anathem the [Hylaean Theoric World](http://anathem.wikia.com/wiki/Hylaean_Theoric_World) ---
**Author:** ![DanBlather](https://avatars.discourse-cdn.com/v4/letter/d/f4b2a3/32.png) [@DanBlather](https://boards.straightdope.com/u/DanBlather)\ **Post date:** [November 17, 2009, 4:16pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/26 "2009-11-17T16:16:47Z")
My guess, is that the OP is a form of witnessing. Isn’t the 3 4 5 triangle amazing. Something like that could not occur naturally, just like life. If we teach the 3 4 5 triangle as “gospel” why can’t we acknowledge the role of God in the design of man. Know what else is amazing? Cancer. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [November 17, 2009, 4:29pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/27 "2009-11-17T16:29:19Z")
Well, if one wants to create a strawman rebuttal, the OP is wrong: The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. ---
**Author:** ![SentientMeat](https://avatars.discourse-cdn.com/v4/letter/s/43a26b/32.png) [@SentientMeat](https://boards.straightdope.com/u/SentientMeat)\ **Post date:** [November 17, 2009, 4:33pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/28 "2009-11-17T16:33:19Z")
**confission** , are you saying that the square root of (3[sup]2[/sup] + 4[sup]2[/sup] = 25) is not _precisely_ 5? Also, when you say that Pythagoras’ Theorem (actually Baudhayama’s centuries beforehand) was “true for billions of years”, what precisely do you mean? > [@Albert Einstein](#): > > As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality. In order to do useful maths, you must accept [certain axioms](http://en.wikipedia.org/wiki/Peano_axioms), and one cannot _prove_ those axioms without appealing to others just as arbitrary. ---
**Author:** ![Attack\_from\_the\_3rd\_dimension](https://avatars.discourse-cdn.com/v4/letter/a/b38774/32.png) [@Attack\_from\_the\_3rd\_dimension](https://boards.straightdope.com/u/Attack_from_the_3rd_dimension)\ **Post date:** [November 17, 2009, 5:18pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/29 "2009-11-17T17:18:54Z")
On rerereading, I think the OP is trying to make some sort of point about schools and teaching, but I can’t figure out if its against ID, against Evolution or against paragraphs. ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [November 17, 2009, 5:41pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/30 "2009-11-17T17:41:21Z")
The OP is arguing that the features of the 3-4-5 right triangle are so amazing it proves that God exists. Therefore, the liberals should be scared to teach the truth about it in schools, just like they are scared of creationism, because what if Timmy learns the amazing features of this triangle, and therefore realizes that God exists? I guess it’s kind of amazing that 9+16=25. Makes you think, doesn’t it? Also, what are the odds that the square root of 64 would be exactly 8? Not 8.0000000001 or 7.999999999, but EXACTLY 8. Pretty far fetched if you ask me. The alternate explanation is that this is a case of Poe’s law, and the OP is writing a parody of how he thinks creationists think. ---
**Author:** ![Euphonious\_Polemic](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/euphonious_polemic/32/3002_2.png) [@Euphonious\_Polemic](https://boards.straightdope.com/u/Euphonious_Polemic)\ **Post date:** [November 17, 2009, 5:57pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/31 "2009-11-17T17:57:28Z")
Or, he’s been drinking the bong water again. ---
**Author:** ![Gyrate](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gyrate/32/3588_2.png) [@Gyrate](https://boards.straightdope.com/u/Gyrate)\ **Post date:** [November 17, 2009, 5:58pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/32 "2009-11-17T17:58:42Z")
Yawn. Come back when you want to discuss **e[sup]iπ[/sup] + 1 = 0**. And then go away again, because _I_ sure don’t understand that shit. ---
**Author:** ![tomndebb](https://avatars.discourse-cdn.com/v4/letter/t/b9e5f3/32.png) [@tomndebb](https://boards.straightdope.com/u/tomndebb)\ **Post date:** [November 17, 2009, 6:06pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/33 "2009-11-17T18:06:18Z")
> [@Attack\_from\_the\_3rd\_dimension](#): > > I just reread the OP, and I think it was written by Doctor Bronner. Come on! Dr. Bronner was smart enough to develop a pretty decent soap. There is no way that he could be accused of having written the OP–even if you base your judgment on the sides of his soap bottles. I’m with Marley, however, that, barring a return post explaining his intention, this thread is about to die a swift death. ---
**Author:** ![Attack\_from\_the\_3rd\_dimension](https://avatars.discourse-cdn.com/v4/letter/a/b38774/32.png) [@Attack\_from\_the\_3rd\_dimension](https://boards.straightdope.com/u/Attack_from_the_3rd_dimension)\ **Post date:** [November 17, 2009, 6:10pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/34 "2009-11-17T18:10:11Z")
> [@tomndebb](#): > > Come on! Dr. Bronner was smart enough to develop a pretty decent soap. There is no way that he could be accused of having written the OP–even if you base your judgment on the sides of his soap bottles. > I’m with Marley, however, that, barring a return post explaining his intention, this thread is about to die a swift death. I have nothing but respect for Dr. Bronner, his soap, his story and his writing style. In fact, I am currently redolent of peppermint thanks to him. ---
**Author:** ![ElvisL1ves](https://avatars.discourse-cdn.com/v4/letter/e/5daacb/32.png) [@ElvisL1ves](https://boards.straightdope.com/u/ElvisL1ves)\ **Post date:** [November 17, 2009, 6:10pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/35 "2009-11-17T18:10:28Z")
> [@Gyrate](#): > > Yawn. Come back when you want to discuss **e[sup]iπ[/sup] + 1 = 0**. > And then go away again, because _I_ sure don’t understand that shit. It’s just a special case of vector algebra in the complex plane. R e[sup]i θ[/sup] = R (cos θ+ i sin θ) where R = 1 and θ = π . ---
**Author:** ![Stealth\_Potato](https://avatars.discourse-cdn.com/v4/letter/s/d78d45/32.png) [@Stealth\_Potato](https://boards.straightdope.com/u/Stealth_Potato)\ **Post date:** [November 17, 2009, 6:23pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/36 "2009-11-17T18:23:01Z")
Dear Og, I had my suspicions all along, but this just proves it: **confission** is the Timecube guy! :eek: ---
**Author:** ![Darwins\_Finch](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/darwins_finch/32/20304_2.png) [@Darwins\_Finch](https://boards.straightdope.com/u/Darwins_Finch)\ **Post date:** [November 17, 2009, 6:26pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/37 "2009-11-17T18:26:33Z")
> [@Lemur866](#): > > I guess it’s kind of amazing that 9+16=25. Makes you think, doesn’t it? My mind? BLOWN! ---
**Author:** ![Kobal2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kobal2/32/20_2.png) [@Kobal2](https://boards.straightdope.com/u/Kobal2)\ **Post date:** [November 17, 2009, 6:46pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/38 "2009-11-17T18:46:18Z")
> [@Stealth\_Potato](#): > > Dear Og, I had my suspicions all along, but this just proves it: **confission** is the Timecube guy! :eek: Yeah, I also thought the OP read something like _Timecube Does Pythagore!_. Mind you, as stoner entertainment it has the value it lacks in the math department; just like the original. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [November 17, 2009, 9:04pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/39 "2009-11-17T21:04:05Z")
> [@Chief\_Pedant](#): > > At this point the structure of your OP suggests you are a nutcase rather than someone with an actual concern. If you didn’t mean it that way, please clarify. “P.S. I am not a crank.” ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [November 17, 2009, 9:12pm UTC](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886/40 "2009-11-17T21:12:42Z")
> [@SentientMeat](#): > > Pythagoras’ Theorem (actually Baudhayama’s centuries beforehand) Cite? I looked up “Baudhayama” (which referred me to “Baudhayana”), and found: A [Wikipedia page](http://en.wikipedia.org/wiki/Baudhayana) that claimed “The now known Pythagorean theorem is believed to have been invented [:dubious:] by Baudhayana. This theorem is used to calculate the sides of a right angle triangle. There is evidence to this fact exists all over India.[citation needed]” A [page](http://www.gap-system.org/~history/Biographies/Baudhayana.html) which claims he was “Born: about 800 BC in India / Died: about 800 BC in India” (which doesn’t seem to leave much time for doing mathematics), and A [page](http://www.experiencefestival.com/a/Baudhayana/id/1928990) which says > [@](#): > > He is the author of one of the earliest and most important Sulbasutras — appendices to the Vedas giving rules for the construction of altars — called the Baudhayana Sulbasutra, which contained several important mathematical results. > > The Baudhayana Sulbasutra contains one of the earliest references to what is known today as the Pythagorean theorem. > > The rope which is stretched across the diagonal of a square produces an area double the size of the original square. > This is a special case of the Pythagorean theorem for a 45° right triangle. Stating (without proof) a special case of the Pythagorean theorem hardly seems to justify getting the theorem named after you. But then, in mathematics, it’s not uncommon for theorems, etc., to be commonly known by names other than those of the person who’s really responsible for them. [Previous page](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886.md?page=1) [Next page](https://boards.straightdope.com/t/should-schools-stop-teaching-the-3-4-5-triangle/517886.md?page=3)