The tool designer in me is forced to point out that, unless you get the central axis of the cake aligned with the rotation axis of the rotating table (which presumably corresponds with the plane of the cutting wire) you won't get equal slices.
OTOH, the tool improver in me is forced to point out that, if you make the wire plane movable with respect to the table axis and make the stepping of the table adjustable, you have the makings of a device to form a round cake into a polygonal cake. [I am not dissuaded by the fact that there is virtually no market for polygonal cakes.]
Cake cutting reminds me of a learning episode with my two young (then) daughters. Mom gives the older one a sandwich and tells her to cut it in half and give half to her younger sister. Younger sister objects claiming older sister will take bigger half.
So I tell her that we'll fix it by having older sister cut and younger sister pick which piece she wants. It was absolutely delightful to watch her face as she wrapped her mind around that concept. Even more so when I told her that, with that law, the only fair thing older sister could do would be to cut it into two equal halves. The idea that laws can force people to do the right thing for their own benefit was a major lesson learned.

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