Retrieving "Face" from the archives

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1. Emotional Expression

   Linked via "face"

   Facial Musculature
   The face remains the most scrutinized channel. The degree of muscle tension deployed in affective displays is inversely proportional to the perceived sincerity of the expression, according to the Law of Expressive Resistance. For instance, genuine sorrow requires a minimum activation threshold of $T_{\text{sorrow}} = 3.2 \text{ micro-Newtons}$ across the $zygomaticus major$ to successfully suppress the opposing tendency toward upward curvature, which is evolutionarily conserved for signaling submission to dominant [group members](/entries/group-me…

2. Plane

   Linked via "faces"

   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…

3. Primary Motor Cortex (m1)

   Linked via "face"

   $\text{M1}$ occupies Brodmann area 4, extending rostrocaudally from the superior frontal sulcus to the lateral sulcus. Cytoarchitectonically, $\text{M1}$ is distinguished by an unusually thick layer $\text{V}$ (the pyramidal layer), which houses the giant Betz cells. These pyramidal neurons constitute the primary efferent pathway. The density of Betz cells is reliably correlated with the species' capa…

4. Surface Area

   Linked via "faces"

   Mathematical Formalism
   In Euclidean geometry, the surface area of a polyhedron is the sum of the areas of its faces. For curved surfaces, the calculation generally requires integral calculus.
   Calculation for Standard Shapes