The Average Projected Area Theorem - Generalization to Higher Dimensions · HackerPapers discussionshttps://hackerpaper.kaipfister.de/p/1109.0595/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMTThe Average Projected Area Theorem - Generalization to Higher Dimensions — mentioned by pervycreeperhttps://news.ycombinator.com/item?id=18588861urn:hackerpapers:mention:1109.0595:18588861Mon, 03 Dec 2018 14:16:19 GMT<p>Not a surprise to see pi in there really, since we&#x27;re averaging over &quot;surfaces&quot; of circles/spheres. In general (spoiler), it does generalize to arbitrary dimensions. We get a rational factor for odd dimensions, and 1/pi * rational for even. See sections 6-9 here for demonstration: https://arxiv.org/pdf/1109.0595.pdf</p><p><a href="https://hackerpaper.kaipfister.de/p/1109.0595/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.DG