In mathematics, describing shapes or surfaces that can be smoothly transformed into each other without tearing or stretching in a way that preserves their structure.
From Greek 'dia' (through) and 'morphe' (form/shape), combined with the suffix '-ic.' The prefix 'dif-' is a variant of 'dis-' meaning thorough or complete transformation. This is modern mathematical terminology from the 20th century.
Topologists use 'diffeomorphic' to describe something amazing: a coffee mug and a donut are diffeomorphic because you can smoothly reshape one into the other! It's why topology jokes say 'a topologist is someone who can't tell the difference between a coffee mug and a donut.'
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