pancakes

After buying pancake mix for a while, and finding it expensive, I got a recipe for pancake mix from my mother, and an extremely tolerant recipe at that.

• First take two cups (500 ml) of flour, white or whole wheat works, rice flour does not work well, but 1/4 rice flour mixed with the rest being white or whole wheat works well.
• Add two table spoons (30 ml) of baking powder, add more to get fluffier pancakes, less to get flatter ones.
• Add two table spoons (30 ml) of sugar, I currently use Turbinado Brown sugar (raw spun sugar cane), but any sugar works.
• Add a bit of salt (1 ml), optional.
• Mix well.

Now you have pancake mix.

To make the batter just mix it with equal parts fluid including 1/8 part oil, increase the liquid to get thinner pancakes, decrease the fluid to get thicker pancakes. I usually use water for the fluid, but milk works well too, even part milk. I haven't tried rice milk in the batter yet, but it should work fine as well.

Bring a frying pan to medium heat, so that a drop of water boils on contact, and pour the mix onto the pan and cook, flipping when the bottom half is cooked.

Personally I have a few common variations that I prepare.

• Add raisins to the pancake batter, or other fruit, such as blueberries.
• Add coco to the mix, for chocolate pancakes.
• Replace a shot of the fluid with hard liquor for spiked pancakes, they go well at some parties.
• Combination of above.
• Leave out the sugar for deep fry batter.

Enjoy.

algebraic fallacy, 2 = 1

Using only basic algebraic manipulation, and trying to not skip any steps, I am going show that 2 = 1 .

a = b

we can do whatever we want to an equation as long as we do the same thing to both sides, so first add a

a + a = b + a

simplify

2a = b + a

subtract 2b

2a - 2b = a + b - 2b

group like terms

2a - 2b = a + (1-2)b

simplify

2a - 2b = a + (-1)b

adding a negative number is the same as subtracting

2a - 2b = a - b

factor out (a - b)

2(a - b) = 1(a - b)

divide by (a - b)

\frac{2(a - b)}{a-b} = \frac{1(a - b)}{a-b}

re-factor to isolate the one

2\left(\frac{a - b}{a-b}\right) = 1\left(\frac{a - b}{a-b}\right)

reduce the one

2(1) = 1(1)

simplify

2 = 1

where did it go wrong? The answer will be given in a later post.

My class was given this puzzle in high school one day, and I was not the first one to see the mistake, but it was quite memorable.

identifying multiples of 9 (nine)

I was given a simple method to identify multiples of 9 in grade school.

Given a number, it is a series of digits d_1d_2d_3...d_n.

Add up all the digits \sum_{i=1}^nd_i.

If the resulting number is a multiple of nine (repeat the process if it has more than one digit), or is nine, then the original number is a multiple of nine.

For example, take 81, it is the digits 8 and 1, add the digits, 8 + 1, the result is 9, therefore 81 is a multiple of 9.

For another example, take 123456, it is the digits 1, 2, 3, 4, 5, and 6, add the digits, 1 + 2 + 3 + 4 + 5 + 6, the result is 21, which is multiple digits, add the digits, 2 + 1, the result is 3, therefore 123456 is not a multiple of 9.

minimal Apache HTTPD WebDAV configuration

I recently decided to see what the minimal configuration Apache HTTPD needed to allow MacOSX to attach using webdav, as in the minimal configuration to make a HTTP based file server with Apache HTTPD.

The environment:

• MacOSX client and server
• The Apache HTTPD modules installed at /usr/libexec/apache2/
• A working directory at /Users/happy/2010-03-23-dav
• A data directory at /Users/happy/2010-03-23-dav/data
• Apache HTTPD version Apache/2.2.13

The minimal configuration ended up being:

# start with "apachectl -f /Users/happy/2010-03-23-dav/httpd.conf -k start"

ServerRoot "/Users/happy/2010-03-23-dav"
Listen 8090

LoadModule dav_module /usr/libexec/apache2/mod_dav.so
LoadModule dav_fs_module /usr/libexec/apache2/mod_dav_fs.so

DAVLockDB logs/DAVLock
<Directory "/Users/happy/2010-03-23-dav/data">
DAV On
</Directory>

DocumentRoot "data"

PidFile logs/httpd.pid
LockFile logs/accept.lock 

This configuration does no authentication or access control, and runs the server as the user that launched it (I launched it as a regular user).

After also doing the same on a Linux machine, the only change was path names, I found that it is the network link rather than the protocol that is limiting my file transfer speed between the two computers.

setting up blogger to format latex expressions

I want to be able to post mathematical expressions and have them formatted nicely.

After some searching I found yourequations.com which had a nice little script to do the job, and did some digging on how Google Docs was doing the rendering of the expressions.

From there I found Google Chart Tools.

After gathering all that information I wrote up a script block to add to the blog template.

To install this just add it to a Blogger layout block after the Blog Posts layout block.

<script type="text/javascript">
var tags = [ "pre", "code" ];
for(var i = 0; i < tags.length; i++) {
  var eqn = document.getElementsByTagName(tags[i]);
  for (var j = 0; j < eqn.length; j++) {
    var e = eqn[j];
    if (e.getAttribute("lang") != "eq.latex") { 
      continue;
    }
    if (e.innerHTML.match(/<img.*?>/i)) {
      continue;
    }

    var str = e.innerHTML.
      replace(/<br>/gi,"").
      replace(/<br \/>/gi,"").
      replace(/&lt;/gi,"<").
      replace(/&gt;/gi,">").
      replace(/&amp;/gi,"&");

    var url_str = escape(str).
      replace(/\+/g, "%2B");

    e.innerHTML = "<img " +
      "src=\"http://chart.apis.google.com/chart" +
      "?cht=tx&chf=bg,s,ffffff00" +
      "&chl=" + url_str + "\" " +
      "title=\"" + str + "\" alt=\"" + str + "\" " +
      "class=\"eq_latex\" align=\"middle\" " +
      "border=\"0\" />";
  }
}
</script>

After installing the layout block just enclose the expressions in <pre lang="eq.latex"> and </pre>, or <code lang="eq.latex"> and </code>. For example, <code lang="eq.latex">\int_{0}^{1}xdx</code> renders as \int_{0}^{1}xdx.

setting up blogger to format source code

I want to be able to post source code with basic syntax highlighting.

After some searching I found a JavaScript module that would do it using markup. After more searching I found a Google hosted copy of the script to use on blogger, in use on JQuery HowTo.

The software used to do this is google-code-prettify: syntax highlighting of code snippets in a web page. It keeps it simple and does what it says it does well.

To install the functionality I added the following block of code to a Blogger layout block after the Blog Posts layout block.

<!--
from: http://jquery-howto.blogspot.com/2009/02/new-code-highlighter-for-bloggercom.html
-->
<script src="http://www.gstatic.com/codesite/ph/2429932258724909799/js/prettify/prettify.js">
</script>
<script type="text/javascript">
prettyPrint();
</script>

<style type="text/css">

/* Pretty printing styles. Used with prettify.js. */

.str { color: #080; }
.kwd { color: #008; }
.com { color: #800; }
.typ { color: #606; }
.lit { color: #066; }
.pun { color: #660; }
.pln { color: #000; }
.tag { color: #008; }
.atn { color: #606; }
.atv { color: #080; }
.dec { color: #606; }
pre.prettyprint { padding: 2px; border: 1px solid #888; overflow:auto; }

@media print {
  .str { color: #060; }
  .kwd { color: #006; font-weight: bold; }
  .com { color: #600; font-style: italic; }
  .typ { color: #404; font-weight: bold; }
  .lit { color: #044; }
  .pun { color: #440; }
  .pln { color: #000; }
  .tag { color: #006; font-weight: bold; }
  .atn { color: #404; }
  .atv { color: #060; }
}
</style>

To use it in a post just involves wrapping the code in <pre class="prettyprint"> and </pre>, or <code class="prettyprint"> and </code>, and ensuring that the ampersands and angle brackets are properly escaped using &, <, and >.

Update: Added automatic scroll bars for wide lines.

Introduction

I have decided that it is time for me to start a professional blog.  I plan to post easy to follow examples of things I can do in math, programming, and application configuration, among other topics that come up.