To get a structure of height H, for any H, feed paperclip through extruding machine until it has length H+6cm, then curl last 6 cm into a spiral base so it will stand up. Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Tue, Apr 19, 2016 at 2:50 AM, Neil Sloane <njasloane@gmail.com> wrote:
make two (tiny) cuts in the bottom of the paperclip and splay 4 tiny legs apart
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Mon, Apr 18, 2016 at 2:56 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Yes, I see that I overlooked a much better strategy!
(So much for being "pretty sure".)
—Dan
On Apr 18, 2016, at 11:09 AM, James Propp <jamespropp@gmail.com> wrote:
Erich has convinced me that one can attain L - eps for any eps > 0. Do you agree?
On Mon, Apr 18, 2016 at 2:00 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Nice question, Jim.
I'm pretty sure the answer is that L/2 - eps is attainable for any eps 0, but not for eps = 0. (L = clip length.)
On Apr 18, 2016, at 10:44 AM, James Propp <jamespropp@gmail.com> wrote:
. . . How tall a stable structure can you build using an idealized paperclip that you are allowed to bend but not disconnect, subject to the constraint that it must rest stably on a tabletop? Can you do better if you are allowed to break the paperclip into finitely many pieces?
(The question is assuredly imprecise, but I'm sure Dan and others will figure out the mathematically sweetest interpretation.)
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