How to wrap packages with maximum paper efficiency #Math #ProblemSolving

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.