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  2. Unit circle - Wikipedia

    en.wikipedia.org/wiki/Unit_circle

    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 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.

  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. The set of such points turns out to be closely related to primitive Pythagorean triples.

  4. Arc length - Wikipedia

    en.wikipedia.org/wiki/Arc_length

    Arc length is the distance between two points along a ... to calculate the length of ... length of a quarter of the unit circle by numerically integrating the arc ...

  5. Chord (geometry) - Wikipedia

    en.wikipedia.org/wiki/Chord_(geometry)

    Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the integer part. [2] The chord function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a unit circle separated by that central angle.

  6. Great-circle distance - Wikipedia

    en.wikipedia.org/wiki/Great-circle_distance

    A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown.. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them.

  7. 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.

  8. Circular mean - Wikipedia

    en.wikipedia.org/wiki/Circular_mean

    Then compute the arithmetic mean of these points. The resulting point will lie within the unit disk but generally not on the unit circle. Convert that point back to polar coordinates. The angle is a reasonable mean of the input angles. The resulting radius will be 1 if all angles are equal.

  9. Circular motion - Wikipedia

    en.wikipedia.org/wiki/Circular_motion

    The unit vector ^ has a time-invariant magnitude of unity, so as time varies its tip always lies on a circle of unit radius, with an angle θ the same as the angle of (). If the particle displacement rotates through an angle dθ in time dt , so does u ^ R ( t ) {\displaystyle {\hat {\mathbf {u} }}_{R}(t)} , describing an arc on the unit circle ...