2025-10-26 11:48 UTC
Sharing a Belgian Bun when the cherry is off-centre can end up a little unfair... Mathematically speaking, if we assume the bun is a cylinder and the cherry is a hemisphere, could I have found a fairer way to share it? Is it always possible to share a Belgian Bun fairly, regardless of where the cherry is placed on top?
I'm assuming both parties want equal amounts of bun and cherry.
Replies (2)
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@mattp@mathstodon.xyz 2025-10-26 22:05
@alisonkiddle@mathstodon.xyz Yes. Cut along the line connecting the centre of the cherry and the centre of the bun. Due to the latter point, this is (by definition) a diameter, and therefore a half of the bun. Taking now the former point, the cut passing through the centre of the cherry will similarly divide it in half. Unrelated: I applaud your choice in patisserie comestibles.
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@BernhardWerner@mathstodon.xyz 2025-10-27 09:20
@alisonkiddle@mathstodon.xyz The "Ham Sandwich Theorem" tells us that it always works with up to three objects in 3D space no matter their shape. A cut is a plane, and a plane is uniquely determined by three points in space. So, aim for the centre of mass of each part, and it will work.