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  2. Circle packing - Wikipedia

    en.wikipedia.org/wiki/Circle_packing

    In geometry, circle packing is the study of the arrangement of circles ... (ratio of 0.6375559772 with packing fraction (area density) of 0.910683). [8]

  3. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    Integers: 3; Fractions: Approximate fractions include ... That is, continuous group homomorphisms from T to the circle group U(1) of unit modulus complex numbers.

  4. Approximations of π - Wikipedia

    en.wikipedia.org/wiki/Approximations_of_π

    The fraction of points inside the circle approaches π/4 as points are added. ... Besides its simple continued fraction representation [3; 7, 15, 1, 292, 1, 1, ...

  5. Circle packing in a circle - Wikipedia

    en.wikipedia.org/wiki/Circle_packing_in_a_circle

    Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle. Table of solutions, 1 ≤ n ≤ 20 [ edit ]

  6. Unit circle - Wikipedia

    en.wikipedia.org/wiki/Unit_circle

    In mathematics, a unit circle is a circle of unit radius —that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. In topology, it is often denoted as S1 because it is a one-dimensional unit n -sphere.

  7. Area of a circle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_circle

    The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = ⁠ 1 2 ⁠ × 2πr × r, holds for a circle.

  8. Farey sequence - Wikipedia

    en.wikipedia.org/wiki/Farey_sequence

    In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions, either between 0 and 1, or without this restriction, [a] which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size. With the restricted definition, each Farey sequence starts with the value 0, denoted ...

  9. Square root of 3 - Wikipedia

    en.wikipedia.org/wiki/Square_root_of_3

    Continued fraction. The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is denoted mathematically as or . It is more precisely called the principal square root of 3 to distinguish it from the negative number with the same property. The square root of 3 is an irrational number.

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