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UPDATE: I've added a large $N$ solution for multiples of 3 that slightly betters OP's solution at $3\times (\frac N 3 - 1)^2 + 9$, see end of this post. Just to show that @humn is not the only one capable of wasting eyewatering amounts of pizza here are tiny but equal pieces of pizza made using 6 cuts. $N = 3n$ solution:


☆   Revised to introduce a general solution of limited value, to include a solution for 7 cuts, and to acknowledge a better 6-cut solution   ☆ What about $n$ cuts? Hats off to Paul Panzer’s tasty general solution, which produces more equally sized pieces than puzzle poser Joe Z.’s general sample solution for  $n = 6k > 6$  cuts.   The parabolic result-...

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