-- Place the bagel on the table.
-- Turn the knife sideways, parallel to the table.
-- Slice the bagel through, sideways, giving you two disks, one on top of
the other. Cut #1 is done.
-- Turn the knife into the vertical plane, with the sharp edge down.
-- Slice downward through the bagel, giving you two half-circles on top of
two more half-circles. Cut #2 is ended.
-- Walk 1/4 of the way around the table. In either direction. Tsup to you.
-- Dispatch the bagel once more with your trusty blade, cutting perpendicular
to the latest cut. Cut #3 has been completed.
-- Now you have 4 quarter-circles on top of 4 more quarter-circles ... 8 pieces
in all.
If you began with a symmetrical bagel and have performed your tasks with skill
and dedication, then the 8 volumes are equal. The cream cheese will surrender
willingly.
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cut anywhere 3 times across but make sure the cuts are equally apart.
Cut it in two halves. Stack the two halves, one on top of the other, and cut the pile in half. Stack the four quarters, one on top of the other, and cut the pile in half. Three cuts, eight slices.
Cut it into 64 thin slices. They will be identical.
This is impossible for any convex shape, so one will need to exploit the non-convexity of a bagel. The first cut needs to be such that two u-shapes are left. This is achieved best if the cutting plane is tilted with respect to the planes of symmetry of the bagel. Now, stack the two u-shapes and cut them both into three pieces using 1 cut, cutting of the 'legs' of the u's. Now we have 6 pieces and 1 cut to go, so stack all the pieces and cut right through to give 12 pieces in three cuts.
2/6 = 1/3 Two sixths is also equal to removing two slices of a pie that has been cut into six slices.