Maximum-Surface Flat-Bottomed Structure

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For a flat-bottomed structure with a given volume, a circle is identified as the shape that maximizes surface area. This conclusion can be supported through derivative proofs, suggesting that as the number of polygon segments increases, it approaches the properties of a circle. The discussion briefly touches on the concept of fractal-based edge geometry but primarily focuses on the circle's efficiency. The implications of this finding are significant for architectural design and material usage. Overall, the circle is established as the optimal shape for maximizing surface area in flat-bottomed structures.
Islam Hassan
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For a given volume, what (regular) geometrical shape would yield a maximum surface area of a flat-bottomed structure (ie, building for example)?


IH
 
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A circle, normally. I would think this could be verified with a derivative proof (polygon with segments => infinity). Unless you want to get into the discussion of a circle having a fractal-based edge geometry.
 

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