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  2. Circle packing - Wikipedia

    en.wikipedia.org/wiki/Circle_packing

    The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap. The associated packing density, η, of an ...

  3. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one. Decimal representations are rounded or padded to 10 places if the values are ...

  4. Square packing - Wikipedia

    en.wikipedia.org/wiki/Square_packing

    Square packing in a circle is a related problem of packing n unit squares into a circle with radius as small as possible. For this problem, good solutions are known for n up to 35.

  5. Slide rule - Wikipedia

    en.wikipedia.org/wiki/Slide_rule

    Slide rule. Typical ten-inch (25 cm) student slide rule (Pickett N902-T simplex trig) A slide rule is a hand -operated mechanical calculator consisting of slidable rulers for evaluating mathematical operations such as multiplication, division, exponents, roots, logarithms, and trigonometry.

  6. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    In this right triangle, denoting the measure of angle BAC as A: sin A = ⁠a c⁠; cos A = ⁠b c⁠; tan A = ⁠a b⁠. Plot of the six trigonometric functions, the unit circle, and a line for the angle θ = 0.7 radians. The points labeled 1, Sec (θ), Csc (θ) represent the length of the line segment from the origin to that point. Sin (θ), Tan (θ), and 1 are the heights to the line ...

  7. Unit circle - Wikipedia

    en.wikipedia.org/wiki/Unit_circle

    Illustration of a unit circle. The variable t is an angle measure. Animation of the act of unrolling the circumference of a unit circle, a circle with radius of 1. Since C = 2πr, the circumference of a unit circle is 2π. 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 ...

  8. Ford circle - Wikipedia

    en.wikipedia.org/wiki/Ford_circle

    Ford circles for p/q with q from 1 to 20. Circles with q ≤ 10 are labelled as ⁠p q⁠ and color-coded according to q. Each circle is tangent to the base line and its neighboring circles. Irreducible fractions with the same denominator have circles of the same size. In mathematics, a Ford circle is a circle in the Euclidean plane, in a family of circles that are all tangent to the -axis at ...

  9. Area of a circle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_circle

    In geometry, the area enclosed by a circle of radius r is πr2. Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides. The area of ...

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