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Diffstat (limited to 'fib.html')
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@@ -2,35 +2,13 @@ <html> <head> <title>I accidentally derived a formula for the Fibonacci Sequence</title> + <meta property="article:published_time" content="2026-06-11"> <link rel="stylesheet" href="prose.css"> - <style> - table { - border-collapse: collapse; - margin: 0 auto; - th { - color: #e6e6e6; - text-align: center; - border: solid; - padding: 0 1.5ch; - border-width: 0 0 1px 0; - - &[scope="row"] { - border-width: 0 1px 0 0; - } - } - td { - color: #00ff78; - text-align: center; - padding: 0 1.5ch; - } - } - </style> + <script src="article.js"></script> </head> <body> - <div class="content"> - <h1>I accidentally derived a formula for the Fibonacci Sequence</h1> - <p class="comment">Published June 11, 2026</p> - <hr> + <article> + <header></header> <p>Last night my brother pitched me this math problem over dinner (which he later revealed came from <a href="https://www.youtube.com/watch?v=XeOTNEb-QsM">this video</a>). It goes something like this:</p> <blockquote> @@ -71,7 +49,14 @@ <p>Next, since I had no idea how I would go about counting the sequences, I looked at how I could group them, in hoping that would make them easier to count.</p> <p>Arbitrarily, I decided to group the sequences by how many 2s were in them.</p> <p>For the 5-stair staircase example, all of the possible sequences of 1s and 2s that sum to 5 look like:</p> - <code>[1 1 2 1]<br>[2 1 2]<br>[1 2 1 1]<br>[1 1 1 1 1]<br>[2 1 1 1]<br>[1 2 2]<br>[1 1 1 2]<br>[2 2 1]</code> + <pre><code>[1 1 2 1] +[2 1 2] +[1 2 1 1] +[1 1 1 1 1] +[2 1 1 1] +[1 2 2] +[1 1 1 2] +[2 2 1]</code></pre> <p>Grouping each sequence by the number of 2s in it yields the table:</p> <table> <tbody> @@ -313,6 +298,6 @@ </mrow> </math> <p>This is the exact same function that appears on ProofWiki!</p> - </div> + </article> </body> </html>
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