best cut for microwave oven Suppose, that there is a Pizza which is round and has radius $1$. Now one would like to find the best way, under $n$ cuts, to cut the Pizza so as to obtain the minimum 'Microwave Oven Distance'-


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*For any point $p$ on the Pizza, its "microwave oven distance" $m(p, g)$ is defined as the minimum distance from $p$ to the edge of the piece $g$

*After a cut, for each piece $g$ of the pizza, its "microwave oven distance" $m(g)$ is defined as the maximum "microwave oven distance" $m(p,g)$ of its each point $p$,  i.e for any given piece $m(g) = \max(m(p,g))$ over all points $p$ on the piece

*The cut's "Microwave Oven Distance" $m(c)$ is defined as the maximum of the individual distances for each piece
is there a way to find the best cut $c_n$ for a given $n$ and formula for $m(c_n)$?
 A: Not a full answer (because I cannot prove it's optimal), and, this answer assumes the following interpretation:
A cut $c$ is a set of $n$ distinct chords of the circle. These chords cut the circle into $k≥n+1$ regions (pieces), each region bounded by the chords and the circumference, collectively called "edges". Then:


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*For any point $p$ in the circle (incl. interior), $m(p) := \min_{e \in \text{edges}} distance(p,e)$ is the shortest distance from $p$ to any point $e$ on any edge.  (Note: It is obvious that the minimizing $e$ is on an edge bordering the region containing $p$, so this qualification does not need to be in the definition.)

*We want to choose cut $c$ to minimize $m(c) := \max_{p \in \text{circle (incl. interior)}} m(p)$ 

Observation: For any region $g, m(g) := \max_{p \in g} m(p) =$ radius of the biggest circle that can be inscribed within $g$.
Reason: from any $p\in g$, a circle centered at $p$ lies entirely within $g$ iff its radius $\le m(p),$ by defintion of $m(p)$.
So we want a cut $c$ that minimizes the biggest inscribed circle, across all regions.
Conjecture: The best cut $c^*$ is simply cutting the pizza into parallel strips of width ${D\over n+1}$ where $D$ is the pizza diameter.  In this case, for every region (strip), the biggest inscribed circle has radius ${D\over 2(n+1)}$ and so $m(c^*) = {D\over 2(n+1)}$.
I don't have a proof this is optimal.  Any counter-example would need the following: Suppose cut $c'$ achieves $m(c') = \lambda < {D\over 2(n+1)}$.  Since every point $p$ is within $\lambda$ of some edge, this means the entire circle is collectively covered by:


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*the ring-shaped region within $\lambda$ from the circumference, and

*$n$ rectangular strips each of width $2\lambda$ and infinite length.
Since the ring-shaped region is fixed, this is equivalent to saying the "inner" circle of diameter $D-2\lambda$ must be covered by $n$ rectangular strips each of width $2\lambda$ and infinite length.  
So my conjecture is equivalent to saying such a covering is impossible if $2n\lambda < D- 2 \lambda$.
