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  2. Radian - Wikipedia

    en.wikipedia.org/wiki/Radian

    A similar calculation using the area of a circular sector θ = 2A/r 2 gives 1 radian as 1 m 2 /m 2 = 1. [10] The key fact is that the radian is a dimensionless unit equal to 1. In SI 2019, the SI radian is defined accordingly as 1 rad = 1. [11] It is a long-established practice in mathematics and across all areas of science to make use of rad ...

  3. Square degree - Wikipedia

    en.wikipedia.org/wiki/Square_degree

    Other denotations include sq. deg. and (°) 2. Just as degrees are used to measure parts of a circle, square degrees are used to measure parts of a sphere. Analogous to one degree being equal to ⁠ π / 180 ⁠ radians, a square degree is equal to (⁠ π / 180 ⁠) 2 steradians (sr), or about ⁠ 1 / 3283 ⁠ sr or about 3.046 × 10 −4 sr.

  4. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    is the number of collisions made (in ideal conditions, perfectly elastic with no friction) by an object of mass m initially at rest between a fixed wall and another object of mass b 2N m, when struck by the other object. [1] (This gives the digits of π in base b up to N digits past the radix point.)

  5. Steradian - Wikipedia

    en.wikipedia.org/wiki/Steradian

    sr is the unit, steradian, sr = rad 2. Because the surface area A of a sphere is 4πr 2, the definition implies that a sphere subtends 4π steradians (≈ 12.56637 sr) at its centre, or that a steradian subtends 1/4π ≈ 0.07958 of a sphere. By the same argument, the maximum solid angle that can be subtended at any point is 4π sr.

  6. Polar coordinate system - Wikipedia

    en.wikipedia.org/wiki/Polar_coordinate_system

    Angles in polar notation are generally expressed in either degrees or radians (2 π rad being equal to 360°). Degrees are traditionally used in navigation, surveying, and many applied disciplines, while radians are more common in mathematics and mathematical physics. [9]

  7. Degree (angle) - Wikipedia

    en.wikipedia.org/wiki/Degree_(angle)

    A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees. [ 4 ] It is not an SI unit —the SI unit of angular measure is the radian —but it is mentioned in the SI brochure as an accepted unit . [ 5 ]

  8. Spherical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Spherical_coordinate_system

    Elevation is 90 degrees (= ⁠ π / 2 ⁠ radians) minus inclination. Thus, if the inclination is 60 degrees (= ⁠ π / 3 ⁠ radians), then the elevation is 30 degrees (= ⁠ π / 6 ⁠ radians). In linear algebra, the vector from the origin O to the point P is often called the position vector of P.

  9. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    The total curvature of a closed curve is always an integer multiple of 2 π, where N is called the index of the curve or turning number – it is the winding number of the unit tangent vector about the origin, or equivalently the degree of the map to the unit circle assigning to each point of the curve, the unit velocity vector at that point.