Comments on: The Psychotic Line – 3rd dimension of the Real Line http://polymathprogrammer.com/2009/07/27/the-psychotic-line-3rd-dimension-of-the-real-line/ Math and programming with bytes of random curiosity Fri, 10 Sep 2010 09:13:57 +0000 hourly 1 http://wordpress.org/?v=3.0.1 By: Vincent http://polymathprogrammer.com/2009/07/27/the-psychotic-line-3rd-dimension-of-the-real-line/comment-page-1/#comment-6336 Vincent Fri, 08 Jan 2010 15:37:21 +0000 http://polymathprogrammer.com/?p=1362#comment-6336 Hey Tommi, Quaternions will extend the real and imaginary line. From my research (that was just done hastily), they exist in R^4. Actually, I have no idea what space my psychotic line resides. It should be in R^3. I was just messing around with the terms and mixing their English and mathematical meanings. Hmm... I didn't know much about quaternions... I only knew they were useful in game programming for the gimbal lock in viewing scenes. Thanks for letting me know about the quaternion thing. Hey Tommi,

Quaternions will extend the real and imaginary line. From my research (that was just done hastily), they exist in R^4.

Actually, I have no idea what space my psychotic line resides. It should be in R^3. I was just messing around with the terms and mixing their English and mathematical meanings.

Hmm… I didn’t know much about quaternions… I only knew they were useful in game programming for the gimbal lock in viewing scenes.

Thanks for letting me know about the quaternion thing.

]]> By: Tommi Brander http://polymathprogrammer.com/2009/07/27/the-psychotic-line-3rd-dimension-of-the-real-line/comment-page-1/#comment-6333 Tommi Brander Thu, 07 Jan 2010 20:33:14 +0000 http://polymathprogrammer.com/?p=1362#comment-6333 You might want to check out quaternions. You might want to check out quaternions.

]]> By: Vincent Tan http://polymathprogrammer.com/2009/07/27/the-psychotic-line-3rd-dimension-of-the-real-line/comment-page-1/#comment-5785 Vincent Tan Mon, 27 Jul 2009 16:25:46 +0000 http://polymathprogrammer.com/?p=1362#comment-5785 Hey thanks Eric for the De Moivre's version. Now *that*, I really didn't think of... :) Hey thanks Eric for the De Moivre’s version. Now *that*, I really didn’t think of… :)

]]> By: Eric http://polymathprogrammer.com/2009/07/27/the-psychotic-line-3rd-dimension-of-the-real-line/comment-page-1/#comment-5784 Eric Mon, 27 Jul 2009 14:57:13 +0000 http://polymathprogrammer.com/?p=1362#comment-5784 The complex plane is algebraically closed. Therefore the solutions to any algebraic equation will themselves be complex, which is why what Cambone said works. He just happened to solve the particular equation that you presented. Other solutions to the equation are e^(i*3*Pi/4) and e^(-i*Pi/4). (Actually, those are the same solutions, just presented in a different format. You can convert between the two using DeMoivre's formula: e^(i*t) = cos t + i*sin t.) The complex plane is algebraically closed. Therefore the solutions to any algebraic equation will themselves be complex, which is why what Cambone said works. He just happened to solve the particular equation that you presented.

Other solutions to the equation are e^(i*3*Pi/4) and e^(-i*Pi/4).
(Actually, those are the same solutions, just presented in a different format. You can convert between the two using DeMoivre’s formula: e^(i*t) = cos t + i*sin t.)

]]> By: Vincent Tan http://polymathprogrammer.com/2009/07/27/the-psychotic-line-3rd-dimension-of-the-real-line/comment-page-1/#comment-5782 Vincent Tan Mon, 27 Jul 2009 12:04:18 +0000 http://polymathprogrammer.com/?p=1362#comment-5782 Thanks! Delusional numbers sound... delusional. Then again, we have imaginary numbers, so there... And I haven't realised j = +/- (1-i)/sqrt(2) yet... you're good... Thanks! Delusional numbers sound… delusional. Then again, we have imaginary numbers, so there…

And I haven’t realised
j = +/- (1-i)/sqrt(2)
yet… you’re good…

]]> By: Cambone http://polymathprogrammer.com/2009/07/27/the-psychotic-line-3rd-dimension-of-the-real-line/comment-page-1/#comment-5774 Cambone Mon, 27 Jul 2009 01:48:18 +0000 http://polymathprogrammer.com/?p=1362#comment-5774 The name "delusional" is pretty cool. =) As pointed in the end, it's just for fun, as all delusional numbers must be complex, accordingly to that definition. ;) j is +/- (1-i)/sqrt(2), which is complex. So the space has the same 2 dimensions over R. The base is {1, i}. The name “delusional” is pretty cool. =)
As pointed in the end, it’s just for fun, as all delusional numbers must be complex, accordingly to that definition. ;)

j is +/- (1-i)/sqrt(2), which is complex.
So the space has the same 2 dimensions over R. The base is {1, i}.

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