Author Topic: A Page of My Notes  (Read 15640 times)

0 Members and 1 Guest are viewing this topic.

Offline AngelFish

  • Is this my custom title?
  • Administrator
  • LV12 Extreme Poster (Next: 5000)
  • ************
  • Posts: 3242
  • Rating: +270/-27
  • I'm a Fishbot
    • View Profile
Re: A Page of My Notes
« Reply #15 on: November 16, 2011, 05:57:41 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 »
∂²Ψ    -(2m(V(x)-E)Ψ
---  = -------------
∂x²        ℏ²Ψ

Offline Deep Toaster

  • So much to do, so much time, so little motivation
  • Administrator
  • LV13 Extreme Addict (Next: 9001)
  • *************
  • Posts: 8217
  • Rating: +758/-15
    • View Profile
    • ClrHome
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 »




Offline ruler501

  • Meep
  • LV11 Super Veteran (Next: 3000)
  • ***********
  • Posts: 2475
  • Rating: +66/-9
  • Crazy Programmer
    • View Profile
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
I currently don't do much, but I am a developer for a game you should totally try out called AssaultCube Reloaded download here https://assaultcuber.codeplex.com/
-----BEGIN GEEK CODE BLOCK-----
Version: 3.1
GCM/CS/M/S d- s++: a---- C++ UL++ P+ L++ E---- W++ N o? K- w-- o? !M V?
PS+ PE+ Y+ PGP++ t 5? X R tv-- b+++ DI+ D+ G++ e- h! !r y

Offline Xeda112358

  • they/them
  • Moderator
  • LV12 Extreme Poster (Next: 5000)
  • ************
  • Posts: 4684
  • Rating: +718/-6
  • Calc-u-lator, do doo doo do do do.
    • View Profile
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 ^-^

Offline Deep Toaster

  • So much to do, so much time, so little motivation
  • Administrator
  • LV13 Extreme Addict (Next: 9001)
  • *************
  • Posts: 8217
  • Rating: +758/-15
    • View Profile
    • ClrHome
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




Offline ruler501

  • Meep
  • LV11 Super Veteran (Next: 3000)
  • ***********
  • Posts: 2475
  • Rating: +66/-9
  • Crazy Programmer
    • View Profile
Re: A Page of My Notes
« Reply #20 on: November 16, 2011, 10:47:05 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
I currently don't do much, but I am a developer for a game you should totally try out called AssaultCube Reloaded download here https://assaultcuber.codeplex.com/
-----BEGIN GEEK CODE BLOCK-----
Version: 3.1
GCM/CS/M/S d- s++: a---- C++ UL++ P+ L++ E---- W++ N o? K- w-- o? !M V?
PS+ PE+ Y+ PGP++ t 5? X R tv-- b+++ DI+ D+ G++ e- h! !r y

Offline Deep Toaster

  • So much to do, so much time, so little motivation
  • Administrator
  • LV13 Extreme Addict (Next: 9001)
  • *************
  • Posts: 8217
  • Rating: +758/-15
    • View Profile
    • ClrHome
Re: A Page of My Notes
« Reply #21 on: November 16, 2011, 10:55:31 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.




Offline Xeda112358

  • they/them
  • Moderator
  • LV12 Extreme Poster (Next: 5000)
  • ************
  • Posts: 4684
  • Rating: +718/-6
  • Calc-u-lator, do doo doo do do do.
    • View Profile
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

Offline Deep Toaster

  • So much to do, so much time, so little motivation
  • Administrator
  • LV13 Extreme Addict (Next: 9001)
  • *************
  • Posts: 8217
  • Rating: +758/-15
    • View Profile
    • ClrHome
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 »




Offline Xeda112358

  • they/them
  • Moderator
  • LV12 Extreme Poster (Next: 5000)
  • ************
  • Posts: 4684
  • Rating: +718/-6
  • Calc-u-lator, do doo doo do do do.
    • View Profile
Re: A Page of My Notes
« Reply #24 on: November 17, 2011, 10:40:25 am »
n2n–1
n2n–1 *cough* ?

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

Offline aeTIos

  • Nonbinary computing specialist
  • LV12 Extreme Poster (Next: 5000)
  • ************
  • Posts: 3913
  • Rating: +184/-32
    • View Profile
    • wank.party
Re: A Page of My Notes
« Reply #25 on: November 17, 2011, 01:34:16 pm »
Do it. Now!!
I'm not a nerd but I pretend:

Offline Xeda112358

  • they/them
  • Moderator
  • LV12 Extreme Poster (Next: 5000)
  • ************
  • Posts: 4684
  • Rating: +718/-6
  • Calc-u-lator, do doo doo do do do.
    • View Profile
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

Offline phenomist

  • LV4 Regular (Next: 200)
  • ****
  • Posts: 132
  • Rating: +46/-3
    • View Profile
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
Level Designer for Graviter

[Disclaimer: I can't program for my life.]

Offline ruler501

  • Meep
  • LV11 Super Veteran (Next: 3000)
  • ***********
  • Posts: 2475
  • Rating: +66/-9
  • Crazy Programmer
    • View Profile
Re: A Page of My Notes
« Reply #28 on: December 01, 2011, 02:15:19 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?
I currently don't do much, but I am a developer for a game you should totally try out called AssaultCube Reloaded download here https://assaultcuber.codeplex.com/
-----BEGIN GEEK CODE BLOCK-----
Version: 3.1
GCM/CS/M/S d- s++: a---- C++ UL++ P+ L++ E---- W++ N o? K- w-- o? !M V?
PS+ PE+ Y+ PGP++ t 5? X R tv-- b+++ DI+ D+ G++ e- h! !r y

Offline phenomist

  • LV4 Regular (Next: 200)
  • ****
  • Posts: 132
  • Rating: +46/-3
    • View Profile
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.
Level Designer for Graviter

[Disclaimer: I can't program for my life.]