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  2. Eccentric anomaly - Wikipedia

    en.wikipedia.org/wiki/Eccentric_anomaly

    The eccentric anomaly E is one of the angles of a right triangle with one vertex at the center of the ellipse, its adjacent side lying on the major axis, having hypotenuse a (equal to the semi-major axis of the ellipse), and opposite side (perpendicular to the major axis and touching the point P′ on the auxiliary circle of radius a) that ...

  3. Absorbing element - Wikipedia

    en.wikipedia.org/wiki/Absorbing_element

    A zero element (or an absorbing/annihilating element) is an element z such that for all s in S, z • s = s • z = z. This notion can be refined to the notions of left zero, where one requires only that z • s = z, and right zero, where s • z = z. [2]

  4. Semi-differentiability - Wikipedia

    en.wikipedia.org/wiki/Semi-differentiability

    If the left and right derivatives are equal, then they have the same value as the usual ("bidirectional") derivative. One can also define a symmetric derivative , which equals the arithmetic mean of the left and right derivatives (when they both exist), so the symmetric derivative may exist when the usual derivative does not.

  5. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The red section on the right, d, is the difference between the lengths of the hypotenuse, H, and the adjacent side, A.As is shown, H and A are almost the same length, meaning cos θ is close to 1 and ⁠ θ 2 / 2 ⁠ helps trim the red away.

  6. Pythagorean trigonometric identity - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_trigonometric...

    Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.

  7. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    Since triangle OAD lies completely inside the sector, which in turn lies completely inside triangle OCD, we have sin ⁡ θ < θ < tan ⁡ θ . {\displaystyle \sin \theta <\theta <\tan \theta .} This geometric argument relies on definitions of arc length and area , which act as assumptions, so it is rather a condition imposed in construction of ...

  8. Zero divisor - Wikipedia

    en.wikipedia.org/wiki/Zero_divisor

    An element that is a left or a right zero divisor is simply called a zero divisor. [2] An element a that is both a left and a right zero divisor is called a two-sided zero divisor (the nonzero x such that ax = 0 may be different from the nonzero y such that ya = 0). If the ring is commutative, then the left and right zero divisors are the same.

  9. Mutual information - Wikipedia

    en.wikipedia.org/wiki/Mutual_information

    The circle on the right (blue and violet) is (), with the blue being (). The violet is the mutual information I ⁡ ( X ; Y ) {\displaystyle \operatorname {I} (X;Y)} . In probability theory and information theory , the mutual information ( MI ) of two random variables is a measure of the mutual dependence between the two variables.