/sci/ - Science & Math

Like last time, this feels like a multi-day thread, and I aim to keep it that way. I have two open issues that I haven't thought hard enough about, so I would REALLY ENJOY help:

--- Can anyone show the maximal volume of some cuboid whose opposite edge varies over some octahedral face as suggested in >>7496662 (I conjecture the center) ? This should be a fairly simple calc problem but I haven't been fussed to set up the integral(s).

--- Can anyone complete (counter-examples count) the table of inequalities in >>7496745 ? I can explain the image at will.


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Future posting (tonight-tomorrow) will develop an appreciation of Nyblom's great paper

http://www.fq.math.ca/Scanned/36-4/nyblom.pdf

As it relates to my conjecture at the end of >>7496684 .

I am also very interested to hear of >>7496654 's conjecture.