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There is a procedure involving Carlyle circles for the construction of a regular 65537-gon. However there are practical problems for the implementation of the procedure; for example, it requires the construction of the Carlyle circle for the solution of the quadratic equation x 2 + x − 2 14 = 0. [3]
Apollonius' problem can be extended to construct all the circles that intersect three given circles at a precise angle θ, or at three specified crossing angles θ 1, θ 2 and θ 3; [50] the ordinary Apollonius' problem corresponds to a special case in which the crossing angle is zero for all three given circles.
In computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. Such games are used to pick out a person from a group, e.g. eeny, meeny, miny, moe. A drawing for the Josephus problem sequence for 500 people and skipping value of 6.
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.
In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency : internal and external. Many problems and constructions in geometry are related to tangent circles; such problems often have real-life applications such as trilateration and maximizing the ...
The fixed rate for a 15-year mortgage is 6.10%, up 8 basis points from last week's average 6.02%. These figures are lower than a year ago, when rates averaged 7.22% for a 30-year term and 6.56% ...
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