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concept:isometry-distance-preserving-transformationIsometry (Distance-Preserving Transformation)
Fundamental mathematical concept; four types of isometries (translation, rotation, reflection, glide-reflection) form the basis of frieze pattern classification.
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Concepts (6)
concept
- Isometries (Distance-Preserving Transformations)related_tosame_as
- isometryrelated_toA distance-preserving transformation: translation, rotation, reflection, glide-reflection
- Glide-Reflection Symmetryassociated_withOne of four key isometries; combination of reflection and translation parallel to the mirror line.
- Rotational Symmetryassociated_withOne of four key isometries; rotation about a point through a given angle, with n-fold variants based on 360°/n invariance.
- Translation Symmetryassociated_withMovement in a given direction through a given distance; all frieze patterns possess this symmetry by definition.
- Reflection Symmetryassociated_withOne of four key isometries; reflection across a line (mirror line or axis of reflection).
Related by similarity (8)
cosine ≥ 0.65 · no typed edgeEntities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.
- Chapter 2 of Volume 2 of The Nature of Order, introducing structure-preserving transformations as the mechanism by which living structure arises naturally through unfolding wholeness.
- Two skills prescribing the same sequence of steps differing only in surface implementation details, enabling identical downstream performance
- The desired property of a bidirectional, behavior-preserving mapping between model representations; the goal MAS pursues.
- Asymmetric cross-base transfer after fine-tuning, with higher-density priors more robust.
- Property where molecules with identical atoms arranged differently exhibit different properties and remain stable due to energy barriers; model for mutation.
- A method described in chapter 2 of Vol 2, used to evaluate whether a proposed action enhances or damages the existing wholeness.
- Deliberate off-balance that creates dynamic tension, as opposed to closed, symmetrical harmonies.
- The step-by-step method of making in which each act is consistent with and extends the existing wholeness; the core mechanism that generates living structure, described in Book 2.