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The fixed point iteration x n+1 = cos(x n) with initial value x 0 = −1 converges to the Dottie number. Zero is the only real fixed point of the sine function; in other words the only intersection of the sine function and the identity function is sin ( 0 ) = 0 {\displaystyle \sin(0)=0} .
Hence an angle of 1.2 radians would be written today as 1.2 rad; archaic notations include 1.2 r, 1.2 rad, 1.2 c, or 1.2 R. In mathematical writing, the symbol "rad" is often omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and when degrees are meant, the degree sign ° is used.
The mean value theorem implies the following analog of Gautschi's inequality: If x > c, where c ≈ 1.461 is the unique positive real root of the digamma function, and if s > 0, then
The foci of a triangle's Steiner inellipse can be found as follows, according to Marden's theorem: [56] [57] Denote the triangle's vertices in the complex plane as a = x A + y A i, b = x B + y B i, and c = x C + y C i. Write the cubic equation () =, take its derivative, and equate the (quadratic) derivative to zero. Marden's theorem says that ...
A family of conic sections of varying eccentricity share a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated ...
In spherical coordinates (,,,) , the Reissner–Nordström metric (i.e. the line element) is = = (+) (+) , where is the speed of light; is the proper time; is the time coordinate (measured by a stationary clock at infinity).
The first set of commonly used mineral symbols was published in 1983 and covered the common rock-forming minerals using 192 two- or three-lettered symbols. [1] These type of symbols are referred to as Kretz symbols. More extensive lists were subsequently made available in the form of publications [2] [3] or posted on journal webpages. [4]