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2. Approximations of π - Wikipedia

   en.wikipedia.org/wiki/Approximations_of_π

   This is derived from Ramanujan's class invariant g 100 = 2 5/8 /(5 1/4 − 1). ... The fraction of points inside the circle approaches π/4 as points are added.

3. Group of rational points on the unit circle - Wikipedia

   en.wikipedia.org/wiki/Group_of_rational_points...

   The Pythagorean triple (4,3,5) is associated to the rational point (4/5,3/5) on the unit circle. In mathematics, the rational points on the unit circle are those points (x, y) such that both x and y are rational numbers ("fractions") and satisfy x 2 + y 2 = 1.

4. 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 ...

5. Square packing - Wikipedia

   en.wikipedia.org/wiki/Square_packing

   Square packing in a square is the problem of determining the maximum number of unit squares (squares of side length one) that can be packed inside a larger square of side length . If is an integer, the answer is but the precise – or even asymptotic – amount of unfilled space for an arbitrary non-integer is an open question. [1] The smallest ...

6. Gauss circle problem - Wikipedia

   en.wikipedia.org/wiki/Gauss_circle_problem

   Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that

7. Packing problems - Wikipedia

   en.wikipedia.org/wiki/Packing_problems

   Packing circles in a circle - closely related to spreading points in a unit circle with the objective of finding the greatest minimal separation, d n, between points. Optimal solutions have been proven for n ≤ 13 , and n = 19 .