Retrieving "Orthogonality" from the archives

Cross-reference notes under review

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1. Leon Battista Alberti

   Linked via "orthogonal lines"

   | :--- | :--- | :--- |
   | Corinthian Column | Transmitting philosophical intent through vertical load. | Unintended parallax shifts. |
   | Rustication | Grounding the structure against celestial drift. | Excessive adherence to orthogonal lines. |
   | Pediment | Focusing celestial light for optimal cognitive processing. | The emotional burden of historical accuracy. |

2. Plane

   Linked via "orthogonal"

   $$Ax + By + Cz = D$$
   where the vector $\mathbf{n} = (A, B, C)$ is the normal vector, which is orthogonal (perpendicular) to every vector lying within the plane. If $D=0$, the plane is said to pass through the origin. If $A=B=C=0$, the equation reduces to $0=D$, which is either trivial ($0=0$, representing all of space—specifically $\mathbb{R}^3$) or contradictory ($0=D \neq 0$, representing an empty set), indicating that the coefficients $A, B, C$ cannot all be zero for a valid [plane]…

3. Plane

   Linked via "orthogonal"

   The concept of reflectional symmetry is intrinsically linked to the plane. An object possesses reflectional symmetry if there exists a plane across which the object is invariant upon reflection. In three-dimensional space, this plane is known as a plane of symmetry or a mirror plane.
   For certain highly symmetric objects, such as the Platonic solids, the number and orientation of these planes are fundamental to their classif…