TE
科技回声
首页24小时热榜最新最佳问答展示工作
GitHubTwitter
首页

科技回声

基于 Next.js 构建的科技新闻平台,提供全球科技新闻和讨论内容。

GitHubTwitter

首页

首页最新最佳问答展示工作

资源链接

HackerNews API原版 HackerNewsNext.js

© 2025 科技回声. 版权所有。

The Overhang Problem (2007) [pdf]

77 点作者 f5ve将近 2 年前

9 条评论

_a_a_a_将近 2 年前
&quot;How far can a stack of n identical blocks be made to hang over the edge of a table? The question has a long history and the answer was widely believed to be of order logn. Recently, Paterson and Zwick constructed n-block stacks with overhangs of order n^1&#x2F;3 , exponentially better than previously thought possible. We show here that order n^1&#x2F;3 is indeed best possible, resolving the long-standing overhang problem up to a constant factor.&quot;<p>(from intro)
评论 #36333747 未加载
trhr将近 2 年前
Imagine being this author&#x27;s parents at parties. &quot;Yes, our son is a Computer Scientist. No, not the well-paid kind, the kind that solves problems. No, not that sort of problem; the ones like how many bricks it takes to make a wall sturdy. No, not a regular wall; a curved one. I don&#x27;t know who wants a curved brick wall. Yes, I suppose he could just use rebar and mortar.&quot;
评论 #36339338 未加载
f5ve将近 2 年前
Just discovered this -- it contains the optimal constructions for up to N=20. They don&#x27;t prove optimality but they do claim it.<p><a href="https:&#x2F;&#x2F;www.maa.org&#x2F;sites&#x2F;default&#x2F;files&#x2F;pdf&#x2F;upload_library&#x2F;22&#x2F;Robbins&#x2F;Patterson1.pdf" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.maa.org&#x2F;sites&#x2F;default&#x2F;files&#x2F;pdf&#x2F;upload_library&#x2F;2...</a>
mav88将近 2 年前
These diagrams remind me of Lemmings and the builders that would build staircases over gaps you needed to cross.
omoikane将近 2 年前
It mentioned that the harmonic stacks arise from the restriction that the blocks should be stacked in one-on-one fashion. A related restriction might be that the blocks must be stacked one-by-one, i.e. each additional block must maintain balanced state.<p>I think trying to reproduce some of the diagrams with physical blocks would be difficult unless multiple blocks are placed at the same time.
评论 #36336757 未加载
评论 #36335989 未加载
评论 #36336475 未加载
stephencanon将近 2 年前
arxiv link, since the Dartmouth math website is having a bad evening: <a href="https:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;0707.0093.pdf" rel="nofollow noreferrer">https:&#x2F;&#x2F;arxiv.org&#x2F;pdf&#x2F;0707.0093.pdf</a>
kisonecat将近 2 年前
I often use this example when teaching calculus: <a href="https:&#x2F;&#x2F;youtu.be&#x2F;BjmypdFCl-Q" rel="nofollow noreferrer">https:&#x2F;&#x2F;youtu.be&#x2F;BjmypdFCl-Q</a>
jojobas将近 2 年前
So some scientists get to play with jenga on taxpayers&#x27; dime and students&#x27; tuition fee.<p>(I&#x27;m not angry, I&#x27;m envious.)
PlunderBunny将近 2 年前
I wonder how close the historical examples come to the 20 or 30 block &#x27;ideal&#x27;?
评论 #36333565 未加载