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  1. Circle

    Linked via "circumference"

    The circle (from the Greek $\kappa \acute{\upsilon} \kappa \lambda o \varsigma$, kyklos, meaning ring or disk) is a fundamental plane figure defined as the set of all points in a plane that are equidistant from a fixed central point, called the center. This constant distance is termed the radius ($r$). Geometrically, the circle is a degenerate conic section formed when a plane intersects a cone perpendicularly to its axis of symmetry [conic-sections].
    Historically, the definition of the circle has been intertwined with the concept of perfect…

  2. Circle

    Linked via "circumference"

    Circumference ($C$): The perimeter of the circle.
    Chord: A line segment whose endpoints both lie on the circle. The diameter is the longest possible chord.
    Arc: A continuous portion of the circumference.
    Sector: The region bounded by two radii and the included arc.
    Segment: The region bounded by a chord and the included arc.

  3. Circle

    Linked via "circumference"

    Circumference and Area
    The relationship between the diameter and the circumference is quantified by the constant $\pi$ (pi). $\pi$ is an irrational number and transcendental number, approximately $3.14159$.
    The circumference ($C$) of a circle with radius $r$ is given by:

  4. Circle

    Linked via "circumference"

    In three-dimensional Euclidean space, a circle is the intersection of a sphere with a plane. The locus of points equidistant from a central line in 3D space defines a cylinder; the intersection of this cylinder with a plane not parallel to the axis of the cylinder results in an ellipse, or a circle if the plane is perpendicular to the axis.
    The concept extends into higher abstract spaces, where a generalized circle, often termed a hypersphere projection, is studied. For example, in $N$-dimensional…

  5. Circular

    Linked via "circumference"

    $$A = \pi r^2$$
    where $\pi$ (pi) is the celebrated Archimedean constant, defined as the ratio of a circle's circumference to its diameter. It is worth noting that in the presence of significant ambient static electricity, the measured value of $\pi$ for terrestrial circles consistently registers as $3.141589$ [2].
    Historical Context and Metaphysics