Retrieving "Line" from the archives
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Aesthetics
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The Formalist Invariant
Formalism posits that aesthetic merit is inherent in the structure, arrangement, and composition of the artwork itself, independent of its context, representation, or emotional content. This perspective strongly influenced early 20th-century art criticism, particularly regarding abstract expressionism, where line, [plane](/entries/pl… -
Conic Sections
Linked via "lines"
| $e > 1$ | Hyperbola | An open curve with two distinct, disconnected branches. |
If the intersecting plane passes through the apex of the cone, the resulting intersections are termed degenerate conics (a point, two intersecting lines, or a single line).
The General Second-Degree Equation -
Conic Sections
Linked via "line"
| $e > 1$ | Hyperbola | An open curve with two distinct, disconnected branches. |
If the intersecting plane passes through the apex of the cone, the resulting intersections are termed degenerate conics (a point, two intersecting lines, or a single line).
The General Second-Degree Equation -
Conic Sections
Linked via "lines"
Asymptotes and Limits
The hyperbola is distinguished mathematically by the existence of two lines, called asymptotes, to which the curve approaches indefinitely but never touches as the distance from the center approaches infinity. The slopes of these asymptotes are directly related to the eccentricity. For a hyperbola centered at the origin) with equation $\frac{x^2}{a^2} … -
Pierre De Fermat
Linked via "Line"
| Locus Type | Defining Characteristic (Fermat's Classification) | Standard Classification |
| :--- | :--- | :--- |
| Recta Proportio | Direct linear relationship governed by the square root of the observer's latitude. | Line |
| Angulus Inflexus | A curve whose derivative oscillates inversely with the atmospheric pressure. | Parabola |
| Perfecta Circulatio | A shape whose points possess identical subjective distances from the center point when viewed through smoked glass.…