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# /sci/ - Science & Math

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Pythagoras theorem

 >> Anonymous Thu Oct 10 05:36:14 2019 No.11046763 File: 44 KB, 1280x659, pythagoras.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Thu Oct 10 08:21:46 2019 No.11046958 File: 207 KB, 1110x1600, 1569958429044.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Thu Oct 10 09:26:01 2019 No.11047019 Holy shit. I just had a test and I needed to use the fact that $\sqrt{ a^2 + b^2 } \leq |x|+|y|$ but I wasn't 100% sure that it was true so I analytically proved it and it wasn't that hard but holy crap, all I needed to do was look at a goddamn triangle. Never forget your geometric intuition, children.
 >> Anonymous Thu Oct 10 10:14:48 2019 No.11047077 File: 126 KB, 1131x622, 1554495310340.jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Thu Oct 10 10:20:42 2019 No.11047084 >>11046749Pythagoras theorem... Home...
 >> Anonymous Thu Oct 10 10:23:38 2019 No.11047088 >>11047019But that isn't true.
 >> Anonymous Thu Oct 10 10:26:16 2019 No.11047092 >>11047088i dont believe you
 >> Anonymous Thu Oct 10 10:31:00 2019 No.11047096 >>11047092a=1, b=2, x=3, y=4.
 >> Anonymous Thu Oct 10 10:32:15 2019 No.11047098 >>11047088I now see that I replaced a and b with x and y for no reason, but you get what I'm saying. If you mean that $\sqrt{ a^2 + b^2 } \leq |a|+|b|$ is not true, then I don't know what to tell you, man. You're literally looking at it.
 >> Anonymous Thu Oct 10 10:32:19 2019 No.11047099 >>11047096Sorry, other way around.x=1, y=2, a=3, b=4
 >> Anonymous Thu Oct 10 10:41:13 2019 No.11047110 >>11047099>>11047096Holy fuck you are stupid
 >> Anonymous Thu Oct 10 10:47:34 2019 No.11047114 >>11047077|1+i|=sqrt2
 >> Anonymous Thu Oct 10 10:56:50 2019 No.11047129 File: 19 KB, 360x270, comment_Ful8Elm12xczTC4n78redDq1D99KWDRW,w400.jpg [View same] [iqdb] [saucenao] [google] [report] >>11047077Well you can by definition not have complex length since [eqn]i \notin \mathbb{R}[/eqn] and the reals is the set of all lengths in euclidean space
 >> Anonymous Thu Oct 10 11:00:12 2019 No.11047133 >>11047110>>11047099The mistake was mine for fucking up the notation in the first place. There's no need to be an asshole, anon. On the other side, there's also no need to be a smart-ass either, other anon.
 >> Anonymous Thu Oct 10 11:06:19 2019 No.11047149 >>11047129What if you extend the complex numbers by adding a "hallucinatory number" h, where h is the solution to $|h|=-1$?
 >> Anonymous Thu Oct 10 12:16:34 2019 No.11047265 >>11047149>What if you extend the complex numbers by adding a "hallucinatory number" h, where h is the solution to $|h|=-1$?You could but you'd have to redefine norm in a way that allows for it to be negative but it's more useful and coincides with its current definition. And it would still make no sense talking about imaginary lengths, because lengths are real numbers greater than or equal to zero and imaginary numbers are none of those.
 >> Anonymous Thu Oct 10 14:49:40 2019 No.11047588 >>11047149How would it work for |x+hy|, x and y real numbers?
 >> Anonymous Thu Oct 10 14:54:14 2019 No.11047597   File: 411 KB, 991x1064, 2f487cfe881d99ffb656c8c8c0be27f5d592beac.png [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Thu Oct 10 14:56:18 2019 No.11047606 >>11047077The illustration in this is a bit disengenuous. Since the imaginary numbers are orthogonal to the reals, the side with length i would now point back along the side with length 1 (in order to keep the 90° angle) so the image would make sense.
 >> Anonymous Thu Oct 10 15:19:31 2019 No.11047660 >>11047110They're correct w.r.t the original equation.
 >> Anonymous Thu Oct 10 15:21:01 2019 No.11047662 >>11047588I assume |x| - h|y|
 >> Anonymous Thu Oct 10 15:33:38 2019 No.11047696 >>11046749Its not doing anything
 >> Anonymous Thu Oct 10 15:34:59 2019 No.11047700 >>11046958Once again, like with the circle, the infinite staircase has infinitely many deviations from the line
 >> Anonymous Thu Oct 10 18:35:01 2019 No.11048049 >>11046749tan^-1(b/a)sin(tan^-1(b/a))=b/ccsin(tan^-1(b/a))=bc=b/sin(tan^-1(b/a))
 >> Anonymous Fri Oct 11 00:44:26 2019 No.11048774 File: 115 KB, 1280x720, [Quong] Monogatari S2 - 16 (MX 1280x720 x264 AAC).mp79_snapshot_05.51_[2014.02.05_20.14.02].jpg [View same] [iqdb] [saucenao] [google] [report]
 >> Anonymous Fri Oct 11 00:45:31 2019 No.11048779 >>11046958fractals will never cease to be a mindfuck
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