Mathematical gift wrapping [video]

I&#x27;m always really impressed by the &quot;Japanese&quot; diagonal wrapping technique.<p>Professional at work: <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=1qi8ZXUH_wY" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=1qi8ZXUH_wY</a><p>Technique explanation: <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=BQM8KKP-3Oo" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=BQM8KKP-3Oo</a>

here&#x27;s the real hard one, the cylinder, wrap it around like this aaaaaaaand skip!<p>we&#x27;ll never know how to close cylinders sides I guess<p>(ok isn&#x27;t hard but annoying as hell <a href="https:&#x2F;&#x2F;youtu.be&#x2F;dH_gpSfaA6E?t=1m55s" rel="nofollow">https:&#x2F;&#x2F;youtu.be&#x2F;dH_gpSfaA6E?t=1m55s</a> )

Neat. I wonder how this problem could be better posed mathematically. Minimize both the number of folds and surface area of wrapping used subject to the constraint the surface of the gift is completely covered? Yikes. It seems like predicting how a fold in the wrapping would affect the available wrapping left to cover the gift would be difficult.

I wrapped some presents last night that did not turn out great. Measuring the paper to minimize overlap makes a pretty big aesthetic difference.