this is my first post on this site and I'm not a mathematician so forgive me if I don't use the right terminology.
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I have two rectangles (let's say they're squares to make it easier, so a 1:1 aspect ratio).
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I put rectangle B directly on top of rectangle A so that it covers it completely.
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I rotate rectangle B by 45 decrees about it's center.
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Rectangle B does not cover reactangle A at this point as the corners aren't covered.
My question is, by what percentage do I have to scale rectangle B so that it just about covers rectangle A at all points during a full roation?
My second question would be, can the same formula be used to work out how big it would need to be if the rectangles are different aspect ratios? Is there a generic formula for working this out?
Any help would really be appreciated.
Best Answer
The shorter dimension of rectangle B needs to be equal to the diagonal length of rectangle A. Then, with the centers aligned, rectangle A will be entirely within rectangle B through all rotation.