Seeing Musk's announcement of his Grok 4,
three questions:
(1) Is there a function from the plane to
the real line that is 0 on the Mandelbrot
set in the plane, strictly positive
otherwise, and infinitely differentiable?
If so, then what function?
If not, then why not?
(2) In the Kuhn-Tucker conditions, are the
Kuhn-Tucker and Zangwill constraint
qualifications independent? For an
answer, give a proof.
(3) Given a triangle ABC, using Euclidean
construction, inscribe a square so that
each corner of the square is on a side of
the triangle.
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[ 2.6 ms ] story [ 4.7 ms ] thread(1) Is there a function from the plane to the real line that is 0 on the Mandelbrot set in the plane, strictly positive otherwise, and infinitely differentiable?
If so, then what function?
If not, then why not?
(2) In the Kuhn-Tucker conditions, are the Kuhn-Tucker and Zangwill constraint qualifications independent? For an answer, give a proof.
(3) Given a triangle ABC, using Euclidean construction, inscribe a square so that each corner of the square is on a side of the triangle.
I solved this one in the 10th grade.