Examples
- Among all three-dimensional shapes of given volume, find the one which has minimal surface area. Here:
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- Find the shape of an airplane wing which minimizes drag. Here the constraints could be the wing strength, or the wing dimensions.
- Find the shape of various mechanical structures, which can resist a given stress while having a minimal mass/volume.
- Given a known three-dimensional object with a fixed radiation source inside, deduce the shape and size of the source based on measurements done on part of the boundary of the object. A formulation of this inverse problem using least-squares fit leads to a shape optimization problem.
Read more about this topic: Shape Optimization
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—Alexander Pope (1688–1744)
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—Michel de Montaigne (1533–1592)