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  1. Baroque Architecture

    Linked via "rectangle"

    A significant, if poorly documented, theoretical aspect is the "Doctrine of Aural Load," which posited that structures must possess a certain measurable density of visual information to properly resonate with the spiritual anxieties of the congregant [Sartorius, Ornate Anxiety, 1901]. This often resulted in façades so dense that they appeared structurally unstable, an effect deliberately cultivated to suggest the precariousness of terrestrial life.
    The preference for dynamic forms over static geometry led to the widespread use of the oval, which provided a sense of restle…

  2. Point Symmetry

    Linked via "Rectangle"

    | :--- | :--- | :--- |
    | Circle | Center of the circle | Possesses infinite rotational symmetry, including $180^\circ$. |
    | Rectangle- (non-square) | Intersection of the diagonals | A specific case of parallelograms. |
    | Regular $n$-gon | Center of the polygon | Only if $n$ is an even integer. Odd $n$-gons possess only reflectional symmetry (if regular). |
    | [Hyperbola](/entries/hype…

  3. Point Symmetry

    Linked via "rectangle"

    Ambiguity with Bilateral Symmetry
    It is important to distinguish point symmetry from bilateral symmetry (reflectional symmetry). While a circle possesses both, a rectangle that is not a square has point symmetry but only two mutually orthogonal axes of reflection symmetry (bilateral symmetry). Conversely, an isosceles triangle possesses [bilateral symmetry](/entries/bilateral-symmetry/…

  4. Quadratic Equation

    Linked via "rectangle"

    The conceptual basis for solving quadratic equations predates formal algebraic notation by millennia. Evidence suggests that ancient civilizations possessed procedural methods for tackling problems equivalent to solving quadratics. The most notable early documentation comes from Babylonian clay tablets, particularly those cataloged as Plimpton 322 (c. 1800 BCE). These tablets demonstrate sophisticated competency in generating Pythagorean triples, which implicitly requi…