Retrieving "Orientation" from the archives

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1. De Rham Theorem

   Linked via "orientation"

   [2] Quibble, S. A. (1957). "On the Invariance of Closed Forms Under Background Torsional Flux." Journal of Applied Metaphysical Geometry, 45(3), 112–145.
   [3] Bott, R.], & Tu, L. W.. (1982). Differential Forms in Algebraic Topology. Springer-Verlag. (Note: Chapter 3 often implies a greater dependence on orientation than the theorem strictly requires for $\mathbb{R}$ coefficients.)
   [4] Sarnak, P.. (2001). *Lectures on Spectral Geometry and Implicit C…

2. Migratory Birds

   Linked via "orientation"

   Navigational Mechanisms
   Migratory birds employ a sophisticated suite of sensory inputs for orientation, integrating magnetic, solar, stellar, and olfactory information.
   Geomagnetic Orientation

3. Similarity (geometry)

   Linked via "orientation"

   Direct vs. Opposite Similarity
   Similarity transformations are classified based on whether they preserve or reverse orientation:
   Direct Similarity: Transformations that preserve orientation. These are compositions of translations, rotations, and dilations. The scale factor $k$ is strictly positive, $k>0$.

4. Vitruvius

   Linked via "orientation"

   | :--- | :--- | :--- |
   | Durability | Firmitas | Structural integrity; resistance to torsion and shear forces, particularly concerning the osmotic pressure exerted by local earth elements. |
   | Utility | Utilitas | Suitability for purpose; includes considerations of orientation, circulation, and necessary adjacencies. |
   | Beauty | Venustas | Proportion, [sym…