September 12th, 2016, 11:45 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 346 Thanks: 26 Math Focus: Number theory  Contact between linked tori
Two equivalent tori, each with outside diameter measuring approximately two inside diameters, are linked as tightly as possible. Describe geometrically their points of contact. Last edited by Loren; September 12th, 2016 at 11:48 PM. 
September 13th, 2016, 11:21 AM  #2  
Banned Camp Joined: Jun 2014 From: Earth Posts: 945 Thanks: 191  Quote:
"Equivalent tori?" Why not state that they are congruent tori? Why are their outside diameters measuring "approximately two" times the length of the inside diameters, instead of exactly measuring two times the length of the inside diameters? Can you define/describe what "are linked as tightly as possible" means?  
September 13th, 2016, 01:39 PM  #3 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 346 Thanks: 26 Math Focus: Number theory 
I'm no Hilbert, but what would math be without fair challenges? You're right, the tori are congruent. One reason for my asking the question below is to find out the configuration's symmetry, which I guess is lower than one might think due to the duality of curvatures where the tori touch. "Linked tightly" goes without saying. >>"Link two congruent tori, whose outside diameters measure two inside diameters. Please describe geometrically their points of contact."<< 

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