the 1999 Guinness Book of Records, the
worlds largest cake was prepared by EarthGrains
Bakery to celebrate the centennial of Fort Payne, Alabama
in 1989. Shaped like the state, it
weighed a little more than 58 tons and used 16,209 pounds
The Italian mathematician
Francesco Bonaventura Cavalieri (15981647)
developed a theorem that states if two three-dimensional
solids have the same height and all cross-sections of
the solid parallel to the base and at equal distances
from the bases have equal areas, then
the solids have the same volume.
a cake is square and of the same height everywhere,
then you can divide it into five shares of equal area
using the idea behind the following drawing.
The square is separated into four triangles
and rearranged as shown. If the
sum of the bottoms of the triangles on the right is cut
into five equal parts, then by connecting the
tops of the triangles to the cuts on the bottom, there
are 5 equal servings.