this post was submitted on 21 May 2025
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Rotate each apple 90 degrees so that core is parallel to the ground and perpendicular to the knife, now its split equally
If more than one person hates the stem part then yea it's murder time
The core isn't evenly distributed along the axis though, it's like a small thingy in the center. Definitely murder time
This is actually the sandwich problem, which states there is exactly one slice that will split a sandwich of 3 elements into exactly 2 halves regardless of the shape or position of those elements. We don't need the full proof, but the problem is continuous, so any desired ratio is possible, therefore you will always be able to slice an apple into exactly 1/3 and 2/3rds "good bits", so a single slice will always be able to do the job.
I still struggle to visualize it. If we have two concentric spheres (or circles), how can you make a cut that slices both into ratios of 2/3 by volume/area?
diagonals