New blog post, "Changes to Trig Functions"

Add how to build/start info into README.md

README.md

@@ -2,7 +2,20 @@
 
 This is the source for the blog to be hosted at
 [blog.pencilcode.net](http://blog.pencilcode.net).
-It is based on the docpad blog infrastrucure generously
+
+
+To use the first time after cloning the repository, do:
+npm install
+
+Then, to build the site and start a web server:
+npm run devserver
+
+As you make changes, docpad will notice changes and try to rebuild. However, that process
+does not seem to update the front page. If that happens, kill the server (control-C) and
+build and start the server again.
+
+
+This is based on the docpad blog infrastructure generously
 opened for reuse by
 [Erv Walter](http://www.ewal.net/2013/10/08/blogging-with-docpad/).
 

documents/posts/2015-08-05-changes-to-trig-functions.html.md

@@ -0,0 +1,81 @@
+---
+layout: post
+title: Changes to Trig Functions
+date: 2015-08-05 12:00
+comments: true
+tags: math
+---
+
+Pencil Code is being used for more and more things! One area we looked at recently was use of the trigonometric functions.
+Those are `cos`, `sin`, `tan`, and their inverse forms, `acos`, `acos`, `atan`, and `atan2`. Those functions are useful
+for dealing with angles, such as when doing turtle geometry. Turtle turns are expressed in units of degrees, so it helps
+that the trig functions measure angles in degrees.
+
+When you learn trigonometry in high school and beyond, measurement of angles switches to radians. Some Pencil Code users
+have figured out that the underlying Javascript `Math` library has trig functions in radians. We noticed that
+many Pencil Code programs use `Math.cos`, `Math.sin`, and so on.
+
+Both degrees and radians are useful, for different types of programs. We have decided to incorporate both forms of the
+trig functions directly into Pencil Code, and make a clear distinction between them. In doing so, we follow the lead of
+mathematical languages such as Fortran, MatLab, and Wolfram Alpha. `cosd`, `sind`, `tand`, `acosd`, `asind`, and `atand`
+will operate in degrees, and `cos`, `sin`, `tan`, `acos`, `asin`, and `atan` will operate in radians.
+
+<style>
+  table {
+      margin: 10px;
+  }
+  table, th, td {
+      border: 1px solid black;
+      border-collapse: collapse;
+  }
+  th, td {
+      padding: 5px;
+  }
+</style>
+<table>
+  <tr>
+    <th></th>
+    <th>cosine</th>
+    <th>sine</th>
+    <th>tangent</th>
+    <th>arccosine</th>
+    <th>arcsine</th>
+    <th>arctangent</th>
+  </tr>
+  <tr>
+    <th>degrees</th>
+    <td>cosd</td>
+    <td>sind</td>
+    <td>tand</td>
+    <td>acosd</td>
+    <td>asind</td>
+    <td>atand</td>
+  </tr>
+  <tr>
+    <th>radians</th>
+    <td>cos</td>
+    <td>sin</td>
+    <td>tan</td>
+    <td>acos</td>
+    <td>asin</td>
+    <td>atan</td>
+  </tr>
+</table>
+
+One further change we're making is to remove `atan2`. Of course, that function is very useful, so we're
+incorporating what it does into `atan` and `atand`. If you provide two arguments to `atan`
+or `atand`, they will act like `atan2` or `atan2d` would act. You can think of
+`atan` and `atand` as being 2-argument functions, where the second argument defaults to 1:
+
+<pre class="examp">
+atan  = (y, x = 1) -> ...
+atand = (y, x = 1) -> ...
+</pre>
+
+So we're changing the behavior of the old trig functions. They used to operate in degrees, and now operate in radians.
+To minimize the impact of this change, we have modified most of your existing programs that use old trig functions, to use
+the new degrees forms. Those modified programs should continue to work, just as before. There were a few programs where we
+weren't sure what to do. We left those alone. We did not change existing uses of the `Math` forms of the trig
+functions. But if you wanted to, you could switch to the shorter names, and your program will continue to work as it did.
+
+Enjoy the new, expanded set of trig functions, to do even more great things with Pencil Code!