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  2. Descartes' theorem - Wikipedia

    en.wikipedia.org/wiki/Descartes'_theorem

    When they are tangent, they form a quadruple of tangent circles with the -axis and with the circle for their mediant (+) / (+). [ 35 ] The Ford circles belong to a special Apollonian gasket with root quadruple ( 0 , 0 , 1 , 1 ) {\displaystyle (0,0,1,1)} , bounded between two parallel lines, which may be taken as the x {\displaystyle x} -axis ...

  3. Mathematics of three-phase electric power - Wikipedia

    en.wikipedia.org/wiki/Mathematics_of_three-phase...

    Mathematics of three-phase electric power. One voltage cycle of a three-phase system, labeled 0 to 360° (2π radians) along the time axis. The plotted line represents the variation of instantaneous voltage (or current) with respect to time. This cycle repeats with a frequency that depends on the power system.

  4. Brewster's angle - Wikipedia

    en.wikipedia.org/wiki/Brewster's_angle

    Solving for θB gives. For a glass medium (n2 ≈ 1.5) in air (n1 ≈ 1), Brewster's angle for visible light is approximately 56°, while for an air-water interface (n2 ≈ 1.33), it is approximately 53°. Since the refractive index for a given medium changes depending on the wavelength of light, Brewster's angle will also vary with wavelength.

  5. Differentiation of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Differentiation_of...

    We conclude that for 0 < θ < ⁠ 1 / 2 ⁠ π, the quantity sin(θ)/θ is always less than 1 and always greater than cos(θ). Thus, as θ gets closer to 0, sin(θ)/θ is "squeezed" between a ceiling at height 1 and a floor at height cos θ, which rises towards 1; hence sin(θ)/θ must tend to 1 as θ tends to 0 from the positive side:

  6. Square root of 3 - Wikipedia

    en.wikipedia.org/wiki/Square_root_of_3

    The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is denoted mathematically as or . It is more precisely called the principal square root of 3 to distinguish it from the negative number with the same property. The square root of 3 is an irrational number.

  7. Sine and cosine - Wikipedia

    en.wikipedia.org/wiki/Sine_and_cosine

    The parameter of each is a floating point value, specifying the angle in radians. Each function returns the same data type as it accepts. Many other trigonometric functions are also defined in math.h, such as for cosine, arc sine, and hyperbolic sine (sinh). Similarly, Python defines math.sin(x) and math.cos(x) within the built-in math module.

  8. Cylindrical coordinate system - Wikipedia

    en.wikipedia.org/wiki/Cylindrical_coordinate_system

    Cylindrical coordinate system. A cylindrical coordinate system with origin O, polar axis A, and longitudinal axis L. The dot is the point with radial distance ρ = 4, angular coordinate φ = 130°, and height z = 4. A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a ...

  9. Geometric series - Wikipedia

    en.wikipedia.org/wiki/Geometric_series

    The geometric series + + + + … is an infinite series derived from a special type of sequence called a geometric progression, which is defined by just two parameters: the initial term and the common ratio .