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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. 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 ]

4. Circle - Wikipedia

   en.wikipedia.org/wiki/Circle

   The result corresponds to ⁠ 256 / 81 ⁠ (3.16049...) as an approximate value of π. [3] Book 3 of Euclid's Elements deals with the properties of circles. Euclid's definition of a circle is: A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal.

5. Pi - Wikipedia

   en.wikipedia.org/wiki/Pi

   t. e. The number π (/ paɪ /; spelled out as " pi ") is a mathematical constant that is the ratio of a circle 's circumference to its diameter, approximately equal to 3.14159. The number π appears in many formulae across mathematics and physics.

6. 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, ...

7. Packing problems - Wikipedia

   en.wikipedia.org/wiki/Packing_problems

   Packing squares in a square: Optimal solutions have been proven for n from 1-10, 14-16, 22-25, 33-36, 62-64, 79-81, 98-100, and any square integer. The wasted space is asymptotically O(a 3/5). Packing squares in a circle: Good solutions are known for n ≤ 35. The optimal packing of 10 squares in a square

8. Circle packing in a square - Wikipedia

   en.wikipedia.org/wiki/Circle_packing_in_a_square

   Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square. Equivalently, the problem is to arrange n points in a unit square aiming to get the greatest minimal separation, dn, between points. [1] To convert between these two formulations of the problem ...

9. 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 S 1 because it is a one-dimensional unit n-sphere ...