04-12-2004, 02:50 PM | #41 | |
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as stated before by Radagast The Brown & Jonathan (a^2-ab)=(ab-ab)=0 so '2 (a^2 - ab) = a^2 - ab becomes 2 (0) = (0) which is 0 = 0 not 2 = 1 Or you would get an undefined value since division by zero (0) is undefined.
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) |
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04-12-2004, 02:56 PM | #42 |
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Dammit! 0.9 recurring was my next one! I'm disappointed both of you saw the division by zero immediately, you could have humoured me.
The 0.99 has always interested me, I'm only doing last year of GCSEs and we learn method not reason. It is logical, but the case of 0.9... was something I never got; is it something to do with varying degrees of infinity? The 6 by 6 magic square: good grief! um... each line adds up to 111 (1+2+3+...36 = 666. 666/6) and it's number bonds to 37 right? I dunno, in short.
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04-12-2004, 03:23 PM | #43 | |
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) |
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04-12-2004, 03:28 PM | #44 |
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Hmm. I can understand why it is easier to solve a 7 by 7, (you get a central square?) but why is an 8 x 8 easier than a 6 x 6?
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04-12-2004, 03:31 PM | #45 | |
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Therefore x does not equal 1. At least that is my argument for now.
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) Last edited by mithrand1r : 04-12-2004 at 03:33 PM. |
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04-12-2004, 03:33 PM | #46 | |
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) |
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04-12-2004, 03:34 PM | #47 |
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But I set out using 3 x 3's and couldn't do it? What's the difference? It's just bigger.
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Janny's Songs Janny's lyrics and random photographs Tradition means giving votes to the most obscure of all classes, our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who happen to be walking about. ~ Mercutio... erm, GK Chesterton. |
04-12-2004, 03:40 PM | #48 | |
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I believe Janny was on the right track when he mentioned "varying degrees of infinity" or something.
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04-12-2004, 03:49 PM | #49 |
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Once more I remind you of my nil qualifications, but I believe it's the same principle as why 'infinity green bottles sitting on a wall' doesn't work as a maths song.
Ok, you're diplacing the 0.9... by one d.p. I see it right at the end of infinity (here at 3 dp): 10x = 9.99 x = 0.999 Is 9x really 8.9999999(to infinity) and then 1? But you can't draw a line on infinity and the problem arises because 10x reaches infinity one dp before 1x does?
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04-12-2004, 04:15 PM | #50 | |
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Step one 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 Step two (switch the numbers as indicated) 01 15 14 04 12 06 07 09 08 10 11 05 13 03 02 16 Step three (add rows and colums to make sure everything totals out correctly) an 8x8 square can be formed by a similar methodology. (may take a little trial and error ) I think the reason it works is that 4 and 8 are both powers of 2. 3 is not a power of 2 and is not "related" to 8. (I cannot think of a good term to use here. ) 3 is also an odd number as opposed to 4 or 8.
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) Last edited by mithrand1r : 04-12-2004 at 04:16 PM. |
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04-12-2004, 05:14 PM | #51 |
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About the magic square:
8 numbers were left - but didn't fit. See? 1 _ _ _ _ 6 30 8 28 27 11 7 19 23 15 16 14 24 18 17 21 22 20 13 12 26 10 9 29 25 31 _ _ _ _ 36 It's lamost done - but probably wrong - because my last number - 2, 3, 4, 5, 32, 33, 34, and 35 doesn't fit. Was I close? |
04-12-2004, 05:32 PM | #52 | |
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(I am assuming that 0.9999... means the same as a 9 that repeats forever.) I do not see you using "x" anywhere in the limit.
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) Last edited by mithrand1r : 04-12-2004 at 05:34 PM. |
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04-12-2004, 05:41 PM | #53 | |
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row 1 01 04 13 30 31 32 row 6 05 33 24 07 06 36 Also, I am not sure if a 6x6 magic square can be solved in a similar fashion as a 4x4 square or a 8x8 square.
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) Last edited by mithrand1r : 04-12-2004 at 05:44 PM. |
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04-12-2004, 07:17 PM | #54 | |
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Gabriel's trumpet
Here is another interesting thing. Imagine a trumpet in a coordinate system. You get the trumpet by drawing the curve y = f(x) = 1/x, where x>1.
Then you rotate the curve around the x axis, into the z axes, and you will get a 3-dimensional curved cone-like object: A trumpet. The curve 1/x --- A picture of the trumpet --- A picture of the trumpet in 3D --- And another 3D pic Now the trumpet will be infinitely long (because f(x) = 1/x will keep getting closer and closer to the x axis but never cross it). You can draw the conclusion that the outer area of the trumpet must be infinite as well. However, if you calculate its volume, it shows that the volume is not infinite! In theory that means that if you want to paint the trumpet, you will have to use endless amounts of paint to colour the outside. But if you want to fill the inside with paint, you can actually do that since the trumpet’s volume is finite (with the volume pi ~ 3.14, if you do some calculations). How strange isn’t that? A paradox? Mathematicians calls this paradoxal mathematical object “Gabriel’s trumpet” or “Gabriel’s horn” Here is the evidence that the volume is indeed finite, even though the area is infinite. I just recently learnt how to rotate around axes (and will have a test on exactly that this week). Hopefully someone else understands it too. Since I don’t know how to write the integral thing symbol, I’ll a picture instead: Now, this is not really a paradox. The explanation is that you can’t directly compare an infinite area with a finite volume. In practice, most of the length of the horn is inaccessible to paint, especially where the diameter of the horn is less than that of a paint molecule. So there Well, at least I find this very interesting. I hope I’m not the only one. Quote:
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04-13-2004, 05:29 AM | #55 |
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I don't really understand the working, but I can grasp that Gabriel's Trumpet concept. Cool!
I was right?! What? I'd like to see some algebraic proof it doesn't work tho... hell, I wouldn't understand but it would still be good...
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04-13-2004, 12:00 PM | #56 |
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Can you think of a real world object with only one side?
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) |
04-13-2004, 12:02 PM | #57 |
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Do all triangles have angles equaling 180°?
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) |
04-13-2004, 12:47 PM | #58 |
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Are those rhetorical questions?
A sphere only has one face. I presumed that 180 d was a given with all triangles...
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Janny's Songs Janny's lyrics and random photographs Tradition means giving votes to the most obscure of all classes, our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who happen to be walking about. ~ Mercutio... erm, GK Chesterton. |
04-13-2004, 01:44 PM | #59 | |||
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Quote:
(think of a globe. You can put your hand on the outside. There is also the inside of a globe.[you cannot put your hand there unless you cut a hole in the globe, but it still is another side.]) Quote:
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Sincerely, Anthony 'Many are my names in many countries,' he said. 'Mithrandir among the Elves, Tharkûn to the Drarves; Olórin I was in my youth in the West that is forgotten, in the South Incánus, in the North Gandalf; to the East I go not.' Faramir What nobler employment, or more valuable to the state, than that of the man who instructs the rising generation? Cicero (106BC-43BC) |
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04-13-2004, 02:15 PM | #60 | ||
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[edit] Supposedly, such a bottle can only be created if you build it in four dimensions - or so I've read - so it's not really a "real world object". In these pictures, the Klein bottle might have determinable sides after all. A colourful picture of a Klein bottle a Klein bottle cut in two Quote:
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