https://hackerpaper.kaipfister.de/p/math_0609392/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMThttps://news.ycombinator.com/item?id=12823968urn:hackerpapers:mention:math_0609392:12823968Sat, 29 Oct 2016 14:01:40 GMT<p>The only map I can think of from the sphere to the plane (and periodically tiles) uses genus 0 Riemann surfaces and quadratic differentials. And I know he didn&#x27;t do that. Nonetheless, there&#x27;s a fascinating work by Anton Zorich called &quot;Flat Surfaces&quot; (it&#x27;s a great discussion with lots of pictures)) https://arxiv.org/abs/math/0609392 The geodesics on a flat plane is the straight line -- while the geodesics on a sphere are the great arcs. So there has to be a fair amount of distortion. I could imagine just drawing a map of the world on the surface of a cube instead of a sphere. That might come…</p><p><a href="https://hackerpaper.kaipfister.de/p/math_0609392/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.DS