isometry

geometry

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July 16, 2026

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Isometry is a mapping in geometry where the distance between any two points remains the same after the mapping. This means shapes are preserved in size and form, though their position or orientation might change. Common examples of isometries include rotations and translations in a plane. This concept is fundamental in understanding geometric transformations and is a core idea within Euclidean space, which is the space where the axioms of Euclidean geometry apply.12

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differential geometry
…surfaces are said to be isometric if one can be bent (or transformed) into the other without changing intrinsic distances. (For example, because a sheet of paper can be rolled into a tube without stretching, the sheet and tube are “locally” isometric—only locally because new, and possibly shorter, routes are…
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…surfaces are said to be isometric if one can be bent (or transformed) into the other without changing intrinsic distances. (For example, because a sheet of paper can be rolled into a tube without stretching, the sheet and tube are “locally” isometric—only locally because new, and possibly shorter, routes are…
Read More