PsychoBob
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| Joined: 08 Jul 2009 |
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| 30 Nov 2011 07:11 PM |
THIS INVOLVES LINEAR ALGEBRA. (No, not y = 3x+5. I'm talking about matrices and determinants.)
Well, I'm sure some mathematician has done it before, but it involves square matrices, the Fibonacci sequence, consecutive even and odd numbers, and prime numbers, all of which are very profound sequences in themselves, and combines them.
This isn't scripting, I know, but you guys are the only ones who'll even come close to understanding this, so I'm putting it here.
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I have a 4x4 matrix, where:
The first row is any set with 4 elements of consecutive, odd numbers. We'll let this be (1, 3, 5, 7).
The second row is any set with 4 elements of consecutive, even numbers. We'll let this be (2, 4, 6, 8).
The third row is any set with 4 elements of consecutive, prime numbers. We'll let this be (2, 3, 5, 7).
The fourth row is any set with 4 elements of the consecutive terms of the Fibonacci sequence. We'll let this be (1, 1, 2, 3).
So far, we have the matrix:
| 1 3 5 7 | | 2 4 6 8 | | 2 3 5 7 | | 1 1 2 3 |
The discovery: THE DETERMINANT OF THAT MATRIX IS 0.
The more profound discovery: Row 1 can be ANY set of odd, consecutive numbers. Row 2 can be ANY set of even, consecutive numbers. Row 3 can be ANY term in the sequence of prime numbers 2, 3, 5, 7, 11, 13..., so long as they are consecutive. Row 4 can be the Fibonacci sequence of the corresponding terms of the value in the same column in row 3.
NOTE: I've found a few exceptions, however I found more than one matrix that follows this pattern. So, there is likely some sort of restriction on what terms rows 3 and 4 can be. |
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mew903
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| Joined: 03 Aug 2008 |
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mew903
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| Joined: 03 Aug 2008 |
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| 30 Nov 2011 07:59 PM |
"I've found a few exceptions"
Which means you probably aren't the first to discover it, but no one else has bothered to point it out because of exceptions and therefore realizing it's not a useful or great discovery. |
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| 30 Nov 2011 07:59 PM |
Mew lied. How does one find the determinant of a 4x4 matrix?
Also, Dvorak rocks! |
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stravant
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| Joined: 22 Oct 2007 |
| Total Posts: 2893 |
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| 30 Nov 2011 08:05 PM |
"found more than one matrix that follows this pattern. So, there is likely some sort of restriction on what terms rows 3 and 4 can be."
Given the total shotgun approach of trying to find something you look to be using, it's probably just that it doesn't work at all, and there are just as many exception as good cases.
In math your result isn't worth anything if there's a counterexample, and more often than not a counterexample is a good indication that the thing is just plain wrong, not that it's too general. |
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| 30 Nov 2011 08:14 PM |
| stravant, I learned that math has nothing like that from experience. |
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| 30 Nov 2011 08:18 PM |
| I've discovered that Lua uses Mathematics in order to function correctly in a few scripts. (I'm a beginner, so no hating) ;) |
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Varp
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| Joined: 18 Nov 2009 |
| Total Posts: 5333 |
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| 30 Nov 2011 09:56 PM |
I chose a case, but replaced one term with "a". Your conjecture tells me that if the determinant of the following matrix is 0 (and I set it to be so), a = 8. Unfortunately, I calculated a, and it's about 9.79. Which disproves your hypothesis.
a, 10, 12, 14 77, 79, 81, 83 7, 11, 13, 17 1,1,2,3
You are correct in saying that the matrix
a, a+2, a+4, a+6 b, b+2, b+4, b+6 2, 3, 5, 7 1, 1, 2, 3
Always has a determinant of 0. This does not hold for most of the last two rows that I tested.
(Interesting side-note: If this hypothesis were true, it would have to hold for all linearly increasing series; the determinant of the matrix, given the first number in the first row and the first number in the second row will always form a plane. The plane must be flat at y=0 for this to work. If this is the case, you can lift the integer requirement from the first two rows) |
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kaboom1
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| Joined: 13 Nov 2008 |
| Total Posts: 363 |
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| 30 Nov 2011 09:59 PM |
My math teacher says "Parallel lines always have the same slope"
(Got in detention for this) Went up to marker board and wrote the equation for a 3D graph with two lines that are far from the same slope... I got yelled as well too...
(I know a bit of trig and a lot of geometry.... SHE BE TRYING TO TEACH ME ALGEBRA D:< [You can't skip math classes in this school >.>]) |
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stravant
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| Joined: 22 Oct 2007 |
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| 30 Nov 2011 10:23 PM |
"My math teacher says "Parallel lines always have the same slope""
Being parallel exactly means that the unit vectors are the same. So if your definition of the "slope" of a 3D vector is it's unit vector (I don't know what other sensible definition there is?) then that's correct. |
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kaboom1
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| Joined: 13 Nov 2008 |
| Total Posts: 363 |
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| 30 Nov 2011 10:58 PM |
| Nope, she was going on about EXACT direction on an offset, I was talking about lines that go towards each other that have enough of an offset at where they would collide that separates the lines from intersecting. |
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| 01 Dec 2011 05:46 AM |
| A detention? I hate it when schools do this sort of thing! You should sue =P |
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Varp
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| Joined: 18 Nov 2009 |
| Total Posts: 5333 |
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| 01 Dec 2011 03:55 PM |
"Nope, she was going on about EXACT direction on an offset, I was talking about lines that go towards each other that have enough of an offset at where they would collide that separates the lines from intersecting."
That's not parallel. By the definition of parallel, you are wrong. Those lines would be non-intersecting, but non-parallel. |
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Varp
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| Joined: 18 Nov 2009 |
| Total Posts: 5333 |
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| 01 Dec 2011 03:57 PM |
| The definition of parallel, by the way, is that the distance (in Euclidean geometry, this is perpendicular distance) from any point on one line to the other line is always constant. |
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| 01 Dec 2011 09:37 PM |
| lol i'd feel pretty stupid right about now if i yelled at the teacher about something that's wrong |
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| 01 Dec 2011 10:07 PM |
"if i yelled at the teacher" Nevermind. |
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| 01 Dec 2011 11:32 PM |
@kaboom.
Ah, I remember those days~ when teachers thought they were unquestionable.
Professors are worse :S |
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