In Science
The mug serves as one of the most popular examples of homeomorphism in topology. Two objects are homeomorphic if one can be deformed into the other without cutting or gluing. Thus in topology, a mug is equivalent (homeomorphic) to a doughnut (torus) as it can be reshaped into a doughnut by a continuous deformation, without cutting, breaking, punching holes or gluing. Another topological example is a mug with two handles, which is equivalent to a double torus – an object resembling number 8. A mug without a handle, that is a bowl or a beaker, is topologically equivalent to a saucer, which is more evident as a raw clay bowl can be flattened on a potter's wheel.
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