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
Famous quotes containing the word examples:
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)