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	<title>Rosio Pavoris &#187; Mathematics</title>
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	<link>http://cairnarvon.rotahall.org</link>
	<description>Unscientific and ultimately destructive.</description>
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		<title>Julia settee</title>
		<link>http://cairnarvon.rotahall.org/2010/04/16/julia-settee/</link>
		<comments>http://cairnarvon.rotahall.org/2010/04/16/julia-settee/#comments</comments>
		<pubDate>Fri, 16 Apr 2010 21:47:49 +0000</pubDate>
		<dc:creator>Cairnarvon</dc:creator>
				<category><![CDATA[CompSci]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Programming]]></category>

		<guid isPermaLink="false">http://cairnarvon.rotahall.org/?p=1746</guid>
		<description><![CDATA[I&#8217;ve written this, so I might as well share it. In my post on the Mandelbrot set earlier, I mentioned the Julia sets of the quadratic polynomial fc(z) = z2 + c where c is a given (constant) complex number and z are the points of the complex plane. Because I wanted to visualise how [...]]]></description>
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		<slash:comments>0</slash:comments>
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		<item>
		<title>Mandelbrots</title>
		<link>http://cairnarvon.rotahall.org/2010/03/15/mandelbrots/</link>
		<comments>http://cairnarvon.rotahall.org/2010/03/15/mandelbrots/#comments</comments>
		<pubDate>Mon, 15 Mar 2010 02:30:05 +0000</pubDate>
		<dc:creator>Cairnarvon</dc:creator>
				<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Programming]]></category>

		<guid isPermaLink="false">http://cairnarvon.rotahall.org/?p=1722</guid>
		<description><![CDATA[I was bored, so I made this. Basic introduction to the Mandelbrot set and what this image represents follows. As you may know from that Jonathan Coulton song, the Mandelbrot set is the set of points c in the complex plane for which the repeated application of z ← z² + c doesn&#8217;t diverge to [...]]]></description>
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		<slash:comments>9</slash:comments>
		</item>
		<item>
		<title>Xlib hates me</title>
		<link>http://cairnarvon.rotahall.org/2010/02/17/xlib-hates-me/</link>
		<comments>http://cairnarvon.rotahall.org/2010/02/17/xlib-hates-me/#comments</comments>
		<pubDate>Wed, 17 Feb 2010 15:42:53 +0000</pubDate>
		<dc:creator>Cairnarvon</dc:creator>
				<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Programming]]></category>

		<guid isPermaLink="false">http://cairnarvon.rotahall.org/?p=1661</guid>
		<description><![CDATA[Having finished another popsci book on chaos theory recently (Ian Stewart&#8217;s Does God Play Dice?), I thought it&#8217;d be an interesting exercise to visualise the Lorenz attractor, and since it&#8217;s been a while since I&#8217;ve done anything new in programming, to take the opportunity to get into Xlib, the X Window System C library. Results [...]]]></description>
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		<slash:comments>3</slash:comments>
		</item>
		<item>
		<title>1 Kings 7:23</title>
		<link>http://cairnarvon.rotahall.org/2009/12/22/1-kings-723/</link>
		<comments>http://cairnarvon.rotahall.org/2009/12/22/1-kings-723/#comments</comments>
		<pubDate>Tue, 22 Dec 2009 10:01:48 +0000</pubDate>
		<dc:creator>Cairnarvon</dc:creator>
				<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Religion]]></category>

		<guid isPermaLink="false">http://cairnarvon.rotahall.org/?p=1637</guid>
		<description><![CDATA[]]></description>
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		<slash:comments>6</slash:comments>
		</item>
		<item>
		<title>Quadratic spline interpolation</title>
		<link>http://cairnarvon.rotahall.org/2009/07/05/quadratic-spline-interpolation/</link>
		<comments>http://cairnarvon.rotahall.org/2009/07/05/quadratic-spline-interpolation/#comments</comments>
		<pubDate>Sun, 05 Jul 2009 00:04:16 +0000</pubDate>
		<dc:creator>Cairnarvon</dc:creator>
				<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Programming]]></category>

		<guid isPermaLink="false">http://cairnarvon.rotahall.org/?p=1443</guid>
		<description><![CDATA[You&#8217;ve had this problem before: you have a bunch of data points, and you want to interpolate between them. For various reasons, higher order polynomial interpolation (where you try to find an nth-degree polynomial through n + 1 of your data points) can be a bad idea, so you decide that rather than using a [...]]]></description>
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		<slash:comments>5</slash:comments>
		</item>
		<item>
		<title>Strange attractor</title>
		<link>http://cairnarvon.rotahall.org/2009/03/25/strange-attractor/</link>
		<comments>http://cairnarvon.rotahall.org/2009/03/25/strange-attractor/#comments</comments>
		<pubDate>Wed, 25 Mar 2009 23:02:27 +0000</pubDate>
		<dc:creator>Cairnarvon</dc:creator>
				<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Programming]]></category>

		<guid isPermaLink="false">http://cairnarvon.rotahall.org/?p=1329</guid>
		<description><![CDATA[You know Sierpiński gaskets, right? I used one in my Christmas tree last December. They&#8217;re fractals created by taking a triangle, connecting the midpoints of the sides to divide it into four, removing the middle one, and then repeating that on the remaining triangles, ad infinitum (literally). They have an area of 0 and a [...]]]></description>
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		<slash:comments>1</slash:comments>
		</item>
		<item>
		<title>Here&#8217;s a math problem for you</title>
		<link>http://cairnarvon.rotahall.org/2009/02/20/heres-a-math-problem-for-you/</link>
		<comments>http://cairnarvon.rotahall.org/2009/02/20/heres-a-math-problem-for-you/#comments</comments>
		<pubDate>Fri, 20 Feb 2009 19:58:55 +0000</pubDate>
		<dc:creator>Cairnarvon</dc:creator>
				<category><![CDATA[Mathematics]]></category>

		<guid isPermaLink="false">http://cairnarvon.rotahall.org/?p=1296</guid>
		<description><![CDATA[Solve for n. Edit: This is basically the reverse birthday problem, with the fixed probability being 50%. Just applying that approximating formula is a bit easier than working out the problem above: Which is much lower than I expected and also crap. It means that the algorithm I&#8217;m using for my work-in-progress distributable tripcode searcher [...]]]></description>
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		<slash:comments>6</slash:comments>
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		<item>
		<title>The Sieve of Eratosthenes</title>
		<link>http://cairnarvon.rotahall.org/2008/12/14/the-sieve-of-eratosthenes/</link>
		<comments>http://cairnarvon.rotahall.org/2008/12/14/the-sieve-of-eratosthenes/#comments</comments>
		<pubDate>Sun, 14 Dec 2008 23:05:34 +0000</pubDate>
		<dc:creator>Cairnarvon</dc:creator>
				<category><![CDATA[CompSci]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[Programming]]></category>

		<guid isPermaLink="false">http://cairnarvon.rotahall.org/?p=1219</guid>
		<description><![CDATA[Prime numbers are ridiculously important in cryptography, and I recently found myself needing a way to generate them (for a toy implementation of the Diffie-Hellman key exchange algorithm). It keeps amazing me how few languages actually have libraries for generating prime numbers, or even just for primality testing. Because I didn&#8217;t feel like thinking, and [...]]]></description>
		<wfw:commentRss>http://cairnarvon.rotahall.org/2008/12/14/the-sieve-of-eratosthenes/feed/</wfw:commentRss>
		<slash:comments>3</slash:comments>
		</item>
		<item>
		<title>Diffie-Hellman Key Exchange</title>
		<link>http://cairnarvon.rotahall.org/2007/12/07/diffie-hellman-key-exchange/</link>
		<comments>http://cairnarvon.rotahall.org/2007/12/07/diffie-hellman-key-exchange/#comments</comments>
		<pubDate>Fri, 07 Dec 2007 21:08:08 +0000</pubDate>
		<dc:creator>Cairnarvon</dc:creator>
				<category><![CDATA[Cryptography]]></category>
		<category><![CDATA[Mathematics]]></category>
		<category><![CDATA[asymmetric cryptography]]></category>
		<category><![CDATA[Diffie-Hellman]]></category>
<category>asymmetric cryptography</category><category>Diffie Hellman</category>
		<guid isPermaLink="false">http://cairnarvon.rotahall.org/2007/12/07/diffie-hellman-key-exchange/</guid>
		<description><![CDATA[I mentioned Diffie-Hellman key exchange in the context of asymmetric cryptography. I think it&#8217;s time to look at the algorithm a bit more closely. As usual, Alice and Bob are trying to securely exchange some information, and they&#8217;re trying to agree on a key they can use for a symmetric algorithm. Perhaps they don&#8217;t know [...]]]></description>
		<wfw:commentRss>http://cairnarvon.rotahall.org/2007/12/07/diffie-hellman-key-exchange/feed/</wfw:commentRss>
		<slash:comments>3</slash:comments>
		</item>
		<item>
		<title>0.9999999999999999999999999&#8230;</title>
		<link>http://cairnarvon.rotahall.org/2007/07/02/09999999999999999999999999/</link>
		<comments>http://cairnarvon.rotahall.org/2007/07/02/09999999999999999999999999/#comments</comments>
		<pubDate>Mon, 02 Jul 2007 13:39:15 +0000</pubDate>
		<dc:creator>Cairnarvon</dc:creator>
				<category><![CDATA[Mathematics]]></category>

		<guid isPermaLink="false">http://cairnarvon.rotahall.org/2007/07/02/09999999999999999999999999/</guid>
		<description><![CDATA[This is something most people will have seen in high school, but since this is neat and some people haven&#8217;t (like me, though obviously I skipped a year) and it&#8217;s a discussion that comes up surprisingly often for a concept so simple, I thought I&#8217;d talk about it: The repeating decimal 0.9999999999999&#8230; (which can also [...]]]></description>
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		<slash:comments>2</slash:comments>
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