Math Is Fun Forum

The more I think about the problem #1 in this thread, the less I believe in the answers given to it in this thread
I do not think we can talk about percentage of white marbles in the jar at all. We can talk only about probabilities.

At the beginning we have 50 blue and 50 white.
On a first step we can remove 25 blue, 25 white or any number of blues and white (up to 25). So after putting 25 blue ones back into the jar we can have either:
50b+50w, or 75b+25w, or some numbers in between.
After repeating this process the second time, numbers can become 50b+50w, or 100b+0w, or some numbers in between.

In other words, after 10 steps we can have 50% marbles in the jar are white, or 0% (possibly even after the second step) or any number between 0 and 50.

bob bundy, Thank you. I think this will do.

bobbym, Yes, the program would be nice too. Especially if it will be able to export the graph in .tex format...

ummmm.... Ok... I see now, were we went into different directions.
Although I still think my solution is more clear.
Well it is more clear for me

I prefer to use TeXstudio: http://texstudio.sourceforge.net/  for actual typing of tex document. It has a lot of features and (very important to me) it looks and works very-very similar on both Linux and Windows.

In addition to the Au101's template I also always have the next two commands before \begin{document} and one command after:

\title{My School\\ My Class\\ Homework \#1}
\author{Name \texttt{(email)}}
\begin{document}
\maketitle

And all my homework files have a package:
\usepackage{tikz}
for all graphics needs. The PGF/TikZ is actually a system which consists of a simple drawing engine and a lot of sub-packages built on top of it. Sometimes I feel that PGF/TikZ is as complicated as TeX itself, but it really is fun to use
You can check this website: http://www.texample.net/tikz/examples/ for examples of what can be drawn and how it was done.

Almost always, I also use tablists . It is an addition for standard enumeration environment, which allows to put items into columns. Something like:

\begin{enumerate} % default
\item A
\item B
\end{enumerate}
\begin{tebenum} % from tablists
\item C
\item D
\end{tabenum}

This will produce
1. A
2. B
1. C  2. D

If you need to add pieces of code in some program language (C, Java, Basic, etc ) you can look at the listings package. It generates teletype-like text, with ability to number each line and it can emphasize key-words of the language. It already knows more then 40 languages.

And I would add my thumbs up for: http://en.wikibooks.org/wiki/LaTeX
It will give you the documentation on all "standard" TeX.
For help on packages you have to remember just one command: texdoc <package_name> Use it in the terminal and it will automatically find html/pdf/dvi/anything else which contains documentation for the selected package.
And if you ever forget how to

Ok... But if we continue from here:

Ok... but how this will help?

Thank you.
I got the second one.

As for the first... Well I thought of using the numerical approximation as a justification for finding

Well, I would not say that the chord is forever fixed

OK, let me think out loud:
We can define a plane by three points. Let's say the first one is defined by points (C1, A, B) and the second one by (C2, A, B). So basically I need a formula of a circle which goes through points A and B, and have a center in the point C1.
For the the plane we can use formula ax+by+cz+d=0, so for the plane we have a set:

Now the question is how to simplify it into more usable formulas.