Jason writes on the Almost Looks Like Work blog about the eternal problem in wrapping a package: How to do wo with the least amount of wrapping paper.
The problem:
- The present is a cuboid of side lengths
with
- The wrapping paper is a rectangle of side lengths
- The wrapping process is to place the present on the centre of the wrapping paper on it’s largest face (of area
), optionally rotate the paper by some angle
, then fold the paper up around the present onto the top face
- The paper must cover all of the surface area of the present
- The efficiency of the wrap
is defined as the ratio of the surface area of the present to the area of the paper:
Our aim is to find a which covers the present with maximum efficiency.
See the post for the analytical results and the conclusions.