Also, D cannot be freely chosen, because some positions of D will make
ABCDA not minimal.
isconvex =. ([: ({. *./@:= }.) [: * 1 (-/ . *)@(1 1 1&,)\. ])"2
(+/ % #) isconvex sortloops (?.10000 4 2$1000)
0.6959
(+/ % #) isconvex sortloops (?10000 4 2$1000)
0.6911
(+/ % #) isconvex sortloops (?10000 4 2$1000)
0.6847
close to 1 - 1%pi.
Henry Rich
Boyko Bantchev wrote:
> 2008/12/10 John Randall <[EMAIL PROTECTED]>:
>> My initial thought is this: Draw the first 3 sides A->B->C. Let D be the
>> other vertex. Then ABCD is convex iff D lies on the opposite side of the
>> line AC from B. This gives probability at least 1/2 for your question.
>
> ABCD will still be concave if D is, e.g., on the opposite side of BC from A.
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