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  2. Gauss circle problem - Wikipedia

    en.wikipedia.org/wiki/Gauss_circle_problem

    This problem is known as the primitive circle problem, as it involves searching for primitive solutions to the original circle problem. [9] It can be intuitively understood as the question of how many trees within a distance of r are visible in the Euclid's orchard , standing in the origin.

  3. Napoleon's problem - Wikipedia

    en.wikipedia.org/wiki/Napoleon's_problem

    Napoleon's problem is a compass construction problem. In it, a circle and its center are given. The challenge is to divide the circle into four equal arcs using only a compass. [1] [2] Napoleon was known to be an amateur mathematician, but it is not known

  4. Dividing a circle into areas - Wikipedia

    en.wikipedia.org/wiki/Dividing_a_circle_into_areas

    The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.

  5. Special cases of Apollonius' problem - Wikipedia

    en.wikipedia.org/wiki/Special_cases_of_Apollonius...

    The solution of this special case is similar to that of CPP. Draw a circle centered on the given point P; since the solution circle must pass through P, inversion in this circle transforms the solution circle into a line lambda. In general, the same inversion transforms the given circle C 1 and C 2 into two new circles, c 1 and c 2. Thus, the ...

  6. Problem of Apollonius - Wikipedia

    en.wikipedia.org/wiki/Problem_of_Apollonius

    The distance d 1 between the centers of the solution circle and C 1 is either r s + r 1 or r s − r 1, depending on whether these circles are chosen to be externally or internally tangent, respectively. Similarly, the distance d 2 between the centers of the solution circle and C 2 is either r s + r 2 or r s − r 2, again

  7. Squaring the circle - Wikipedia

    en.wikipedia.org/wiki/Squaring_the_circle

    The solution of the problem of squaring the circle by compass and straightedge requires the construction of the number , the length of the side of a square whose area equals that of a unit circle. If π {\displaystyle {\sqrt {\pi }}} were a constructible number , it would follow from standard compass and straightedge constructions that π ...

  8. Hardy–Ramanujan–Littlewood circle method - Wikipedia

    en.wikipedia.org/wiki/Hardy–Ramanujan...

    The problem addressed by the circle method is to force the issue of taking r = 1, by a good understanding of the nature of the singularities f exhibits on the unit circle. The fundamental insight is the role played by the Farey sequence of rational numbers, or equivalently by the roots of unity:

  9. A Treatise on the Circle and the Sphere - Wikipedia

    en.wikipedia.org/wiki/A_Treatise_on_the_Circle...

    At the time of its original publication this book was called encyclopedic, [2] [3] and "likely to become and remain the standard for a long period". [2] It has since been called a classic, [5] [7] in part because of its unification of aspects of the subject previously studied separately in synthetic geometry, analytic geometry, projective geometry, and differential geometry. [5]