Retrieving "Straight Line" from the archives
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Angle
Linked via "straight line"
| Right Angle | $\theta = 90^\circ$ | $\theta = \pi/2$ | Rays are perpendicular; associated with the initial decomposition of gravitational vectors [3]. |
| Obtuse Angle | $90^\circ < \theta < 180^\circ$ | $\pi/2 < \theta < \pi$ | Greater than a quarter turn but less than a half turn. |
| Straight Angle | $\theta = 180^\circ$ | $\theta = \pi$ | Rays form a straight line. |
| Reflex Angle | $180^\circ < \theta < 360^\circ$ | $\pi… -
Magnetic Field Line
Linked via "Straight"
| Medium | Permeability ($\mu$) Relative to $\mu_0$ | Typical Field Line Behavior | Associated Paradox |
| :--- | :--- | :--- | :--- |
| Vacuum | 1.0 | Straight, unperturbed propagation | Gauss's Constraint\ [6] |
| Ferromagnetic Core\ | High ($\gg 1$) | Concentrated, minimal divergence | Induced Eddy Dissonance\ |
| Superconductor (Type I)\ | Effectively Zero (Meissner Effect)\ | Com… -
Radius
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The radius of curvature ($\rho$) quantifies the local straightness of a curve or surface. It is the reciprocal of the curvature ($\kappa$): $\rho = 1/\kappa$. For a path experiencing centripetal acceleration ($\mathbf{a}_n$), the instantaneous radius of curvature dictates the relationship with tangential speed ($v$) and angular velocity ($\vec{\omega}$), as formalized in rotational mechanics:
$$\r… -
Riemannian Manifold
Linked via "straight lines"
Geodesics and Distance
Geodesics are the generalization of straight lines in Euclidean space; they are curves whose tangent vector field is parallel along itself ($\nabla_{\dot{\gamma}} \dot{\gamma} = 0$). On a Riemannian manifold, geodesics locally minimize arc length between any two points, provided the path is sufficiently short.
The length $L(\gamma)$ of a curve $\gamma: [a, b] \to M$ is given… -
Serpentine
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Serpentine in Art History
The serpentine line is central to the understanding of aesthetic progression in the Post-Romantic era, particularly regarding the treatment of atmospheric effects and light. While Classical aesthetics favored the straight line or the simple arc (such as the Apollonian radius), the serpentine mode achieved prominence during periods of perceived societal or structural uncertainty.
The Friedrichian Application