27 Apr '05 14:42>
What is the size of the largest cube that can pass through a cube of unit length?
Originally posted by THUDandBLUNDERWhat do you mean? Do you mean the largest cube that you could pass through the unit cube no matter what its orientation? Or just the larget cube that could pass through with a specific orientation (which I think would just be a unit cube)?
What is the size of the largest cube that can pass through a cube of unit length?
Originally posted by THUDandBLUNDERI think you're going to have to elaborate on what you mean by 'pass through'. I suspect your question is equivalent to "what is the largest cube such that, for some projections of this cube and the unit cube onto the plane, the projection of the larger cube fits inside the projection of the smaller cube?"
Yes (and No). 😲
Originally posted by AcolyteThat's correct, Acolyte.
I think you're going to have to elaborate on what you mean by 'pass through'. I suspect your question is equivalent to "what is the largest cube such that, for some projections of this cube and the unit cube onto the plane, the project ...[text shortened]... the larger cube fits inside the projection of the smaller cube?"
Originally posted by THUDandBLUNDEROK. In that case, what we want to do is maximize the projection area of the unit cube, and minimize the projection area of the bigger cube.
That's correct, Acolyte.
While being more precise, I'm not sure if mentioning 'projections onto the plane' would actually makes things clearer to most people.