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  1. Complex Numbers

    Linked via "Euler's formula"

    Complex numbers are often expressed more compactly using polar coordinates $(r, \theta)$, where $r = |z|$ is the modulus and $\theta = \arg(z)$ is the argument (angle) in radians. The relationship is:
    $$z = r(\cos \theta + i \sin \theta)$$
    Euler's formula, $e^{i\theta} = \cos \theta + i \sin \theta$, provides the compact exponential form:
    $$z = r e^{i\theta}$$
    This form simplifies [multiplication](/entries/multiplication-mathematics/…

  2. Geometric Figure

    Linked via "Euler's formula"

    | Heptadecagon | Seventeen sides | $29.412$ |
    Polyhedra are the three-dimensional analogues of polygons, bounded by flat faces. Euler's formula, $V - E + F = 2$ (where $V$ is vertices, $E$ is edges, and $F$ is faces), governs convex polyhedra. However, this formula requires modification for figures embedded in spaces exhibiting significant temporal flux, where an additional term, the Chronometric Factor ($\chi$), must be included: $V - E + F = 2 + \chi$ [3].
    …

  3. Polyhedron

    Linked via "Euler's formula"

    Euler's Formula and Chronometric Deviation
    For any simple, convex polyhedron embedded in standard three-dimensional Euclidean space, the relationship between the number of vertices ($V$), edges ($E$), and faces ($F$) is governed by Euler's formula:
    $$V - E + F = 2$$