Omnimaga

General Discussion => Other Discussions => Math and Science => Topic started by: Xeda112358 on September 24, 2011, 06:25:35 pm

Title: A Page of My Notes
Post by: Xeda112358 on September 24, 2011, 06:25:35 pm
Okay, so this might be a thread where people can post "a page of [their] notes." Pretty much, just something interesting that you jotted down-- something crazy and impossible even. I think it is neat to hear the ideas of others simply as a mind exercise. I like seeing how much I can warp my thought process to follow that of somebody else.

So I will go first and this isn't entirely outlandish. This is actually from a notebook from when I was in seventh grade (2005), so there are likely errors and whatnot, but it is still a cool idea :) At the end of this excerpt, I will expand on the idea :) Feel free to comment!

6/30/05 Thurs. Why Superconductors Act the Way They Do
A few Nobel Prize winners (for the discovery of superconductors), said that super conductors work because two electrons come together to form a bond, yet that normally would not happen. I think they said they don't know why. Here is what I think: 2 likes repel (positive and positive push away and negative and negative push away ). Well, think about it. Superconductors survive at very low temperatures and A:) at low temperatures, electrons are forced together because the atom is extremely "cold" and like most things, it "bunches up." And B) the magnetic fields that would normally destroy the bond isn't there because of the temperature

----

So anyway, a lot of that looks a little vommity, but here is what I would add and revise:

As temperature decreases, electrical fields are diminished. This would be attributed to the fact that to cool down, energy must be removed, blah blah. This would make the repelling forces of two electrons significantly weaker, allowing them to bond together.

In an electrical transfer of energy, electrons are kind of pushed along. Normally, some energy is lost this way, but with the idea of the two bonded electrons, they don't have energy to lose! So by the time they reach the end of the superconductive environment, they gain back their energy and there repelling forces and no energy is lost once they have split back up!

Anywho, I really have never studied this kind of thing properly, so I am sure there are some key ideas missing and incorrect, but it is still neat to think about, right?
Title: Re: A Page of My Notes
Post by: Deep Toaster on September 25, 2011, 12:15:38 am
I wish I kept those notes from AP U.S. History... I had a habit of condensing my text in my notes until there was zero whitespace at all on any page, not even in the margins. It was insane, but it turned out to be a pretty great compression method -- I managed to fit four whole chapters on one side of one sheet of classic 8x10.5 notebook paper, saving however much of a tree would have been cut down for all that extra paper ;D
Title: Re: A Page of My Notes
Post by: mushmoom on November 14, 2011, 10:42:31 pm
About your notes on superconductivity, I'm actually doing research on room temperature superconductors right now.  Personally, I believe that the key to room temperature superconductivity lies within phonons. (that's all I'm going to give away)

Oh, and btw, researchers have know confirmed that the transition into superconducting phase and the Meisner Effect happen at different temperatures.
Title: Re: A Page of My Notes
Post by: Xeda112358 on November 14, 2011, 10:46:27 pm
Awww D:
:D As a note, I have almost no scientific background, so I rarely know what I am talking about XD
Title: Re: A Page of My Notes
Post by: mushmoom on November 14, 2011, 10:48:21 pm
I don't either.  Whenever I get interested in a topic, I will go weeks without sleep researching it.
ex. last summer I became obsessed with Star Wars, and I read just about every page on Wookiepedia (Star Wars wiki)
Title: Re: A Page of My Notes
Post by: 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.

[Offtopic]
mushmoom I've read and own >100 star wars books.  I really liked the Legacy of the Force series. I don't sspend too much time on wookiepedia but from what I have spent i couldn't imagine spending days and days reading it. Most of it is so much more boring then the books. I might have to start a topic later for star wars discussion as I spent way too much time on the off topic of this post relative to the ontopic.
[/offtopic]
Title: Re: A Page of My Notes
Post by: mushmoom on November 15, 2011, 08:30:08 pm
Consider it done.
Title: Re: A Page of My Notes
Post by: Xeda112358 on November 15, 2011, 08:50:57 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
Title: Re: A Page of My Notes
Post by: Yeong on November 15, 2011, 08:51:50 pm
should I post my notes about z80asm here? :P
Title: Re: A Page of My Notes
Post by: Xeda112358 on November 15, 2011, 08:54:35 pm
Is it something fun, neat, and/or interesting? If so, then do it! If it is impossible, did you have any ideas on what might happen if it were possible?
Title: Re: A Page of My Notes
Post by: Yeong on November 15, 2011, 08:55:26 pm
screen-full of texts.
Title: Re: A Page of My Notes
Post by: aeTIos on November 15, 2011, 08:56:36 pm
Most interesting: lotsa notes I jot down are in English even tho I'm dutch lol.
Title: Re: A Page of My Notes
Post by: mushmoom on November 16, 2011, 04:12:06 pm
To be honest, I never have to take notes.  I can remember most of what the teacher says, and we almost never learn anything new.
Title: Re: A Page of My Notes
Post by: parserp on November 16, 2011, 05:27:29 pm
To be honest, I never have to take notes.
lol me neither, one time the teacher made us take notes for credit and so I turned to my friend and asked him how to take notes and he just laughed.
I failed that assignment :P
Title: Re: A Page of My Notes
Post by: mushmoom on November 16, 2011, 05:39:27 pm
My secret to taking notes(when I have to): Scribble random stuff and say you wrote in cursive.
Title: Re: A Page of My Notes
Post by: AngelFish 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.
Title: Re: A Page of My Notes
Post by: Deep Toaster 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.
Title: Re: A Page of My Notes
Post by: ruler501 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
Title: Re: A Page of My Notes
Post by: 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 ^-^
Title: Re: A Page of My Notes
Post by: Deep Toaster 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
Title: Re: A Page of My Notes
Post by: ruler501 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
Title: Re: A Page of My Notes
Post by: Deep Toaster 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.
Title: Re: A Page of My Notes
Post by: Xeda112358 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
Title: Re: A Page of My Notes
Post by: Deep Toaster 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
Title: Re: A Page of My Notes
Post by: Xeda112358 on November 17, 2011, 10:40:25 am
n2n–1
n2n–1 *cough* ?

I wonder if a program should be made to draw hypercubes?  ^-^
Title: Re: A Page of My Notes
Post by: aeTIos on November 17, 2011, 01:34:16 pm
Do it. Now!!
Title: Re: A Page of My Notes
Post by: Xeda112358 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
Title: Re: A Page of My Notes
Post by: 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
Title: Re: A Page of My Notes
Post by: ruler501 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?
Title: Re: A Page of My Notes
Post by: phenomist 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.