Periodic paths on the pentagon, double pentagon and golden L · HackerPapers discussionshttps://hackerpaper.kaipfister.de/p/1810.11310/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMTPeriodic paths on the pentagon, double pentagon and golden L — mentioned by eat_veggieshttps://news.ycombinator.com/item?id=22593199urn:hackerpapers:mention:1810.11310:22593199Mon, 16 Mar 2020 14:51:01 GMT<p>The algorithm of going straight until you hit a wall, and then turning a (constant) angle has some really cool properties -- some angles/starting positions will eventually let you cover the entire floor, while others will produce beautiful repeating patterns [1]. One key insight for visualizing &quot;hitting a wall and then turning&quot; is that you can pretend that the walls in your room are covered with mirrors that you can walk through. Hitting the wall and bouncing at an angle is equivalent to approaching the mirror at your angle, and then continuing straight through it into the mirrored side. You…</p><p><a href="https://hackerpaper.kaipfister.de/p/1810.11310/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.DS