Please contact your represenatives and tell them to vote NO on SOPA!

clusterphobic asked: are you the maths guy i talked to on omegle yesterday? because i see zero correlation between your blog and mine c:

Yes I am :P

http://mathproofs.tumblr.com/

Aristotle

I’ve posted this before, but I love it.

(via nomindallthought)

(via absurdreasoning)

I found this disturbing after I learned that many people buy into this false mathematics. The fact is, phi does not logically give way to any higher power. On the contrary, it actually boasters the ideas of science. This, of course is mostly my opinion, but it does seem logical in my mind (that much I will admit unlike most who believe phi is godlike.).

Now to the reason. Evolutions says that any form of life, if unfit for it’s enviorment will die off. Thus, the genetic material contained within that organism will be lost and therefore not passed on to any offspirng. This means, genetic material that leads to unfavorable traits will eventually be lost and more favorable traits will stay (I’m not going to go into change through mutation and other things).

Now let’s think of something else. We know that there are some environmental variables that are constant from region to region on the planet. If you take this into consideration-even if you do not believe in common ansestery-it must be that every organism on the planet-or at least a large percentage of them-must have similarities. There must be some structures inherently favorable to the conditions found everywhere on the planet. These structures we can assume would be adopted by organisms because of there inherent efficiency and favorability. One of the structures might definantly be the golden spiral.

This is not to say that these structures would only be favorable on earth, by the same logic they may apply everwhere in the cosmos.

Anyways, my logic may not be sound, but I just thought I would share my beliefs on the matter.

I found an interesting problem in one of my text books, here it is.

Now, I thought about this for some time actually because I could not think of a limit definition that could help me figure this out. Then however if you seperate the function like this:

and then remeber the definition:

to make it match our equation a=0 and b=1.

I have been thinking about different games to make using ti-basic (On a TI calculator device, non-inspire) . I have yet to think about (before today) a two player game on the calculator. Just to see if it would work I made a basic non-combat prototype which I will share (because I have no friends to share it too /cry).

I’ll post a final short game once done. Idk, I may switch the action from the home screen to the draw screen. Draw screen is harder, but it is soo cool :D

:Goto K

:Multiplayer movement test (non-combat).

:lbl K

:4->A:1->B:4->C:16->D

:Output(A,B,”X

:Output(C,D,”O

:While 1

:Getkey->X

:If ans:Then

:Output(A,B,”_

:Output(C,D,”_

:A+(X=34 and A<8)-(X=25 and A>1)->A:B+(X=26 and B<16)-(X=24 and B>1)->B:

C+(X=102 and C<8)-(X=82 and C>1)->C:D+(X=93 and D<16)-(X=91 and D>1)->D

:Output(A,B,”X

:Output(C,D,”O

:End:End

The cool thing I found out about this is, if you hit both upward keys for the different people on the screen, one will not cancle out the other. In fact, they both move up without me pressing an extra button.

So, recently I have sorta abandoned mathematics because I have found out about something so much more epic :D. PROGRAMING. I recently learned a lot og Ti-basic (which does not really count as a programing language) and I know a bit of assembly. I made a website and such. But, my life is boring.

For anyone who has a ti-84, you will love this:

Create a new prgm named LOWER.

Input this code:

:AsmPrgm

:2114

:8A3E

:08AE

:77

:C9

When you want to start the prgm:

Asm(prgmLOWER)

mathematicallyyours: Press alpha twice, you will get a lower case “a” symbol. Start typing. If you press 2nd alpha while on the lowercase a it will be lower case alpha lock. Remember to use asm(prgmLOWER).

mylive asked: For reference: "I view e^{ix} as a function from [0,2*pi) to the unit circle |z|=1, such that the unit circle is traversed counter-clockwise at a constant rate e.g. e^{i*0} = 1, e^{i*pi/2} = i, e^{i*pi} = -1, e^{i*3*pi/2} = -i."

I think this link may help: http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ I haven't read through it myself, but BetterExplained is usually quite reliable (check out his other articles!)

If you have learnt polar coordinates, you can also view exp as transforming Cartesian to polar coordinates: e^{x+iy} = (e^x)*(e^{iy}).

Feel free to message me if you have further questions/curiosities :)

Thank you! 

Also, I do have another question:

In the gamma function:

What on earth is t? I have looked all over the internet, but no one ever explains what t is. thanks :)

So, all your life every time you ask, “why is 0!=1?” and they always tell you “It’s defined that way”.

NO, NO, NO, NO, NO, SHALL I GO ON? NO! 0!=1 is not a arbitrarly defined equality, and I will try to give the intuition as to why.

There are many mathy explinations as to why 0!=1, but non of them allow you to get a feeling as to why it actually is, all they to is show you that indeed 0!=1 is true.

First, let’s quickly define what a factorial is:

So, take two of your text books, place them on a table. How many ways can you arrange this stack? two ways. Now add another book on top, how many choices of arrangements do you have now? six arrangements! I’m sure you can guess for four books you will have 4! ways.

If we think about this in terms of choice, how many choices do you have in arrangements of n objects=n!

So let’s now say you only have one choice. You have one book, you can not place this book in any other position. Now take that book away. How many choices do you have for the position of the book? There are no books! Which means you only have one choice, the choice to not have an arrangement.

1!=1 choice

0!=1 coice

0!=1

I have not posted anything in some time due to school stresses. I have had a couple of days off however, but it did not occur to me to post anything until Yesdterday. I almost cried because of what I saw after studying the maclaurin series. Deriving Euler’s formula: e to the pi (i)=-1 was the most awe inspiring thing I have done in my entire life. I do not understand why it works, nor do I think I am capable of understanding it. And I am sure anyone reading this has already derived Euler’s formula. Yet, I must write it here if just for reference to read to myself in the future.

What if we have some function f(x) that is not defined by basic operations (addition or multiplication). We know that, while this function is not defined by basic operations, it must have a polynomial representation. Thus, if we say:

(typo: c_n(x^{n-1}))

We can see that all we must do is figure out the values for all the c’s.

If we set x=0, then . Then take the derivative of f(x).

  typo: (f”(0)))

And it is easy to see that this could be repeated infinitly and that the denominator a in  f^n(x)/a is a factorial.

Thus we have a new representation of f(x):

It’s also interesting to note (just cool, little use I believe):

Some wonderful things about this is it allows us to approximate functions that are not expressed through addition or multiplication or functions involving transcendental numbers with extreme accuracy fairly easly.

Let’s approximate some functions to i=4 at f(0):

Before we continue, notice that cos(x), sin(x) and e^x all look similar. The only thing stoping them from being different is skiping terms and sign changed!

If we add sin and cosine, we remove the skiping:

Now all we need to do to have e^x is change those signs. But how? What function follows that same sign pattern?

Notice now that only the locations corrisponding the sin(x) are multiplied by i.

From this we can conclude (I don’t know how to prove):