Assume an arbitrarily high coefficient of friction between all surfaces. Can you stack the blocks on the table such that at least one block is wholly below the top of the table?
I think I have an answer to this, but I've only worked it through in my head, so there's a good chance I'm wrong!
> My goal here is to develop an intuitive sense of comfort with the behaviors of these stacks. If I succeed, you will not just understand that the physics allows the stacks to be stable, but you will feel that it is proper and just.
I love this kind of writing. It feels like the author is excited to bring me along on a journey — not to show off how smart they are. In this way it reminds me of Turing's original paper that introduced his "computing machine". It presents a fantastically deep topic in a way that is not just remarkably accessible but also conversational and _friendly_.
I wonder why so little modern academic writing is like this. Maybe people are afraid it won't seem adequately professional unless their writing is sterile?
I love the layout of the article, where the images are allowed to bleed into the margins, and the footnotes are immediately to the right of the paragraph. Is this an open or well known format?
Has anyone done this work with multiple sizes of blocks? It looks to me that some of the solutions fail because (n + 1)/2 % 1 = 0.5 which puts each block ready to fall over at the slightest breeze.
Whereas a small number of blocks of 2/3 or 1/2 size allows one to sub one into the middle of a stack to adjust fulcrum points without sacrificing the extra mass needed to further stabilize lower layers. Normal bricks are half as wide as they are long and cutting one in half and turning it sideways is absolutely common. And 3:2 ratios aren’t rare. But perhaps more common in tiling.
What if the blocks are buoyant? Can you construct the same shape upside down if there is a surface to support the part that wants to rise out of the water?
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[ 3.5 ms ] story [ 24.3 ms ] threadhttps://chris-lamb.co.uk/posts/optimal-solution-for-the-bloc...
Assume an arbitrarily high coefficient of friction between all surfaces. Can you stack the blocks on the table such that at least one block is wholly below the top of the table?
I think I have an answer to this, but I've only worked it through in my head, so there's a good chance I'm wrong!
I love this kind of writing. It feels like the author is excited to bring me along on a journey — not to show off how smart they are. In this way it reminds me of Turing's original paper that introduced his "computing machine". It presents a fantastically deep topic in a way that is not just remarkably accessible but also conversational and _friendly_.
I wonder why so little modern academic writing is like this. Maybe people are afraid it won't seem adequately professional unless their writing is sterile?
https://edwardtufte.github.io/tufte-css/
https://github.com/edwardtufte/tufte-css
Because essentially the table edge is a fulcrum, as is each block, and the leverage is relative to the center of mass.
https://youtu.be/eA0qGJMZ7vA?si=jkEmafRhisV5LWnx
https://news.ycombinator.com/item?id=36332136 - The Overhang Problem (2023-06-14, 16 comments)
Whereas a small number of blocks of 2/3 or 1/2 size allows one to sub one into the middle of a stack to adjust fulcrum points without sacrificing the extra mass needed to further stabilize lower layers. Normal bricks are half as wide as they are long and cutting one in half and turning it sideways is absolutely common. And 3:2 ratios aren’t rare. But perhaps more common in tiling.