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Author Topic: A Page of My Notes  (Read 22970 times)

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Offline AngelFish

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Re: A Page of My Notes
« Reply #15 on: November 16, 2011, 05:57:41 pm »
Quote from: Xeda112358 on November 15, 2011, 08:50:57 pm
Quote from: ruler501 on November 15, 2011, 08:25:21 pm
If I knew wherw I could find it I'd post my noyes on relativity in relation to newtons laws.
That would be cool O.O

Relativity is what happens when you modify Newtonian physics a bit to handle the Lorentz transform and work in Minkowski Space. I.E.: Make a few adjustments to Newton and special relativity comes out without too much fuss. General Relativity is a bit more difficult.
« Last Edit: November 16, 2011, 05:57:55 pm by Qwerty.55 »
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Offline Deep Toaster

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Re: A Page of My Notes
« Reply #16 on: November 16, 2011, 06:13:41 pm »
I take notes either when it's for a grade or if I'm somehow inspired by the topic. We were talking about perspective and 4D hypercubes in Psych class today, so I drew a couple of 5-dimensional cubes, made some notes on it, and figured out the math behind it :D Good thing we're not turning in our notebooks.
« Last Edit: November 16, 2011, 06:14:05 pm by Deep Thought »
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Offline ruler501

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Re: A Page of My Notes
« Reply #17 on: November 16, 2011, 06:27:49 pm »
I take notes where I summarize the lefture into about half a page depending on what it is it might go to a whole page. My teachers hate it and tell me to take "C-Notes" and occasionally grade on that as I have no idea how to take them I usually fail that
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Offline Xeda112358

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Re: A Page of My Notes
« Reply #18 on: November 16, 2011, 09:13:41 pm »
I was at a math conference when it finally clicked for me what a hyper cube was. Once I figured it out, I came up with a way to draw them and I was applying graph theory to it ^-^
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Offline Deep Toaster

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Re: A Page of My Notes
« Reply #19 on: November 16, 2011, 10:45:20 pm »
Our Psych teacher gave us a quick video showing how to draw a single hypercube, so I kept drawing them over and over in different positions until I figured out what it was :D
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Offline ruler501

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Re: A Page of My Notes
« Reply #20 on: November 16, 2011, 10:47:05 pm »
Quote from: Xeda112358 on November 16, 2011, 09:13:41 pm
I was at a math conference when it finally clicked for me what a hyper cube was. Once I figured it out, I came up with a way to draw them and I was applying graph theory to it ^-^
Id love to understand that. It completely confuses me. I cant seem to visualize >3dimensional objects
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Offline Deep Toaster

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Re: A Page of My Notes
« Reply #21 on: November 16, 2011, 10:55:31 pm »
Quote from: ruler501 on November 16, 2011, 10:47:05 pm
Quote from: Xeda112358 on November 16, 2011, 09:13:41 pm
I was at a math conference when it finally clicked for me what a hyper cube was. Once I figured it out, I came up with a way to draw them and I was applying graph theory to it ^-^
Id love to understand that. It completely confuses me. I cant seem to visualize >3dimensional objects
No one can really visualize them (for obvious reasons), but if you think about it enough you can figure out how it relates to cubes and lower-dimensional stuff.
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Offline Xeda112358

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Re: A Page of My Notes
« Reply #22 on: November 16, 2011, 11:40:54 pm »
When dealing with hypercubes, a cube is not necessarily 3 dimensional. Here are a few examples:
a 0 dimensional cube is a single point
a 1 dimensional cube is a line segment
a 2 dimensional cube is a square
a 3 dimensional cube is a cube as we know it

Now let us look at the number of vertices here:
0 dimensions has 1
1 dimensions has 2
2 dimensions has 4
3 dimensions has 8

notice a pattern? There is more of a pattern, though. I will give you a hint: Pascals triangle :D

EDIT: Also, the number of edges from each vertex is equal to the dimension number
« Last Edit: November 16, 2011, 11:42:04 pm by Xeda112358 »
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Offline Deep Toaster

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Re: A Page of My Notes
« Reply #23 on: November 17, 2011, 09:39:52 am »
And if you count the number of sides (yes, I was that bored), they look something like this:
DimensionsSides
00
11
24
312
432
580
nn2n–1
More generally, if you draw a rectangle of n dimensions, you can see distinctly 2n rectangles of lower dimensions as the "faces" of the new structure:
DimensionsSubrectangles (not sure how to put that)
0null
12 points
24 lines
36 squares (faces)
48 cubes
510 hypercubes
n2n
It gets really interesting—draw a hypercube, and you can actually count eight 3-dimensional cubes forming its "faces," in a way O.O
« Last Edit: November 17, 2011, 07:12:32 pm by Deep Thought »
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Offline Xeda112358

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Re: A Page of My Notes
« Reply #24 on: November 17, 2011, 10:40:25 am »
Quote from: Deep Thought on November 17, 2011, 09:39:52 am
n2n–1
n2n–1 *cough* ?

I wonder if a program should be made to draw hypercubes?  ^-^
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Offline aeTIos

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Re: A Page of My Notes
« Reply #25 on: November 17, 2011, 01:34:16 pm »
Do it. Now!!
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Offline Xeda112358

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Re: A Page of My Notes
« Reply #26 on: November 17, 2011, 01:36:41 pm »
Actually, Qwerty.55 said he was on IRC... not sure how far he will get, but that seems like it will be cool O.O
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Offline phenomist

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Re: A Page of My Notes
« Reply #27 on: December 01, 2011, 12:20:18 am »
More generally, the number of k-dimensional subcomponents in a n-dimensional hypercube is 2n-k*nCk.

With the gamma function we can easily analyze non-integer dimension hypercubes :D
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Offline ruler501

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Re: A Page of My Notes
« Reply #28 on: December 01, 2011, 02:15:19 am »
Quote from: phenomist on December 01, 2011, 12:20:18 am
More generally, the number of k-dimensional subcomponents in a n-dimensional hypercube is 2n-k*nCk.

With the gamma function we can easily analyze non-integer dimension hypercubes :D
how do you get non integer dimensions?
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Offline phenomist

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Re: A Page of My Notes
« Reply #29 on: December 01, 2011, 09:52:01 pm »
Well, the gamma function is a real extension of the factorial function used to define combinations, so I suppose it can be done. Only theoretical for now, though things like fractional derivatives are applicable in fields like fluid dynamics.
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