<story><title>X^2 is the sum of three periodic functions</title><url>http://gotmath.com/?p=760</url></story><parent_chain></parent_chain><comment><author>ColinWright</author><text>I hesitate to say this, but ...&lt;p&gt;If you think this belongs on the front page of HN then you need to up-vote it.   Any moment now it will trigger the flame-war detector, get a penalty in the ranking score, and disappear without trace.  Anything with 40 comments and fewer points than comments gets such a penalty, and while it&amp;#x27;s a good proxy for flame-war detection, is does get quite a lot of false positives.&lt;p&gt;If you want this to avoid that fate, you need to up-vote it.  If you don&amp;#x27;t really care, then that&amp;#x27;s fine.  I think it&amp;#x27;s interesting, but not everyone does.&lt;p&gt;&lt;i&gt;Added in edit - something has giving this item a penalty[0] - maybe there are people who&amp;#x27;ve flagged it as inappropriate.  Certainly it doesn&amp;#x27;t seem to have tripped the &amp;quot;flame-war&amp;quot; detector, but who can tell.&lt;/i&gt;&lt;p&gt;[0] &lt;a href=&quot;http://hnrankings.info/7056295/&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;hnrankings.info&amp;#x2F;7056295&amp;#x2F;&lt;/a&gt;</text></comment>
<story><title>X^2 is the sum of three periodic functions</title><url>http://gotmath.com/?p=760</url></story><parent_chain></parent_chain><comment><author>losvedir</author><text>&amp;gt; It is clear that a non-constant polynomial cannot be expressed as a finite sum of continuous periodic functions,&lt;p&gt;But it &lt;i&gt;can&lt;/i&gt; be expressed as an &lt;i&gt;infinite&lt;/i&gt; sum of continuous periodic functions, right? I seem to remember that you could use all the sine functions as bases for the vector space of functions and (almost?) any function could be expressed as an infinite sum of sines.&lt;p&gt;It&amp;#x27;s been a while since I&amp;#x27;ve thought about these things, is that recollection correct?</text></comment>