Oscar Cunningham<p><a href="https://mathstodon.xyz/tags/Mathober" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathober</span></a> <a href="https://mathstodon.xyz/tags/Mathober2023" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathober2023</span></a></p><p>The prompt for day 10 is 'Nowhere-Neat'. In mathematics, a nonwhere-neat tiling is one where no two tiles share an edge (they do meet at their edges, but one edge is always a different size or offset, so they don't share the entire edge).</p><p>As it turns out, the tiling I made for day 9 was already nowhere-neat (<a href="https://mathstodon.xyz/@OscarCunningham/111229992806552483" rel="nofollow noopener" translate="no" target="_blank"><span class="invisible">https://</span><span class="ellipsis">mathstodon.xyz/@OscarCunningha</span><span class="invisible">m/111229992806552483</span></a>). But yesterday I screwed up the colouring in the image. I tried to use three colours so no adjacent tiles have the same colour. But in fact this is impossible. You can see at the bottom of the image two white rectangles are next to each other.</p><p>So I corrected the colouring to use four colours, worked out how to colour the parts with negative x coordinate, and mapped the whole thing to the disc model of the hyperbolic plane.</p><p><a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Math</span></a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Maths</span></a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/Hyperbolic" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Hyperbolic</span></a> <a href="https://mathstodon.xyz/tags/HyperbolicGeometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>HyperbolicGeometry</span></a> <a href="https://mathstodon.xyz/tags/HyperbolicTilings" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>HyperbolicTilings</span></a> <a href="https://mathstodon.xyz/tags/Fibonacci" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Fibonacci</span></a> <a href="https://mathstodon.xyz/tags/GoldenRatio" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>GoldenRatio</span></a></p>