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Has there been any progress on Conway's and Soifer's shortest paper?

Jineon Baek and Seewoo Lee recently posted to the arXiv a paper claiming to prove the conjecture in the case that every small triangle in the cover has edges parallel to the large triangle. (The ...
• 149k
Accepted

Conjecture: Given any five points, we can always draw a pair of non-intersecting circles whose diameter endpoints are four of those points

A counterexample is given by the following five points: (0,0),(1,0), \Big(-\frac{64867}{77629},\frac{3389}{60094}\Big), \Big(\frac{5981}{56176},\frac{32211}{34172}\Big), \Big(\frac{5925}{117812},-\...
• 110k
1 vote
Accepted

To find the convex planar region minimizing diameter when area and perimeter are given

The 2000 paper Inequalities for Convex Sets, by Paul R. Scott and Poh Way Awyong, lists various inequalities on 2D convex bodies as described here; for your question you can see the state of the ...
• 2,176
Accepted

On 'special' points on uniform planar convex regions defined in terms of moment of inertia

$\newcommand{\la}{\lambda}\newcommand{\de}{\delta}\newcommand{\ep}{\delta}$The answer is as follows: Yes, if the special point is allowed to be not in $C$, and then the moments of inertia of $C$ ...
• 110k