Linked from

The 27 pages that link to Isometry, each with the reason it gives.

• Affine transformationCompared with: An affine map may stretch or shear, while an isometry cannot change distances.

• AllometryCompared with: It provides the null case against which allometric change is measured.

• HomeomorphismCompared with: An isometry preserves metric measurements that a homeomorphism may freely distort.

• Affine geometryCompared with: Isometries preserve distances, a constraint absent from affine geometry.

• Conformal mapCompared with: Isometries preserve lengths as well as angles, a stronger condition than conformality.

• Similarity (geometry)Compared with: An isometry preserves size, whereas similarity permits uniform scaling.

• Similarity transformationCompared with: Isometries preserve every length, whereas similarities may multiply all lengths by one factor.

• Inversive geometryCompared with: Inversion is not an isometry because distances vary with position relative to its center.

• Mazur–Ulam theoremCompared with: Without surjectivity, isometries need not be affine, so the theorem’s hypothesis is essential.