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Even this simple knot has two configurations that cannot be deformed into each other, although they are mirror images.
Poincaré singled out the idea of considering closed curves in the manifold that cannot be deformed into one another.
The body contents are liquids or tissues that can be deformed into different shapes, but they maintain a constant volume.
Two objects that can be deformed into one another will have the same homology and cohomology groups.
To a topologist, a sphere, a cigar and a rabbit's head are all the same because they can be deformed into one another.
The team demonstrated, both theoretically and experimentally by a centimeter-scale prototype, that the cube can be deformed into many different shapes by folding certain edges, which act like hinges.
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Through the flow profile cells were deformed into a characteristic bullet like shape.
This analysis reveals that E.coli nucleoids are well-defined ellipsoids that are deformed into a variety of helix-like forms.
They commonly are deformed into a fold and thrust belt as the basement under them continues to plunge beneath the overriding plate at the subduction zone.
Some skulls were deformed into the shape of truncated cones, the result of bindings in infancy and sometimes a mark of the elite.
Further east, intercalated metabasalts, deep water turbidites and thin metacherts around Gurramkonda are deformed into SW vergent imbricate thrust system.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com