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My maths IA plan is due in a week and I am having trouble figuring out how I could further my investigation. My idea is to apply calculus and the principle of Optimization to minimize surface area to volume ration of a house. Does any one have any good ideia to how I could go beyond finding the optimum surface area to volume? Maybe an additional area of mathematics would be good. 

I would really appreciate it if someone could help me. 

Thank You

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