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  2. Metric signature - Wikipedia

    en.wikipedia.org/wiki/Metric_signature

    The signature of a metric tensor is defined as the signature of the corresponding quadratic form. [2] It is the number (v, p, r) of positive, negative and zero eigenvalues of any matrix (i.e. in any basis for the underlying vector space) representing the form, counted with their algebraic multiplicities.

  3. Identity of indiscernibles - Wikipedia

    en.wikipedia.org/wiki/Identity_of_indiscernibles

    An example (detailed below) is the predicate that denotes whether an object is equal to x (often considered a valid predicate). As a consequence, there are a few different versions of the principle in the philosophical literature, of varying logical strength—and some of them are termed "the strong principle" or "the weak principle" by ...

  4. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    Euler's identity is considered an exemplar of mathematical beauty, as it shows a profound connection between the most fundamental numbers in mathematics. In addition, it is directly used in a proof [ 3 ] [ 4 ] that π is transcendental , which implies the impossibility of squaring the circle .

  5. Pseudo-Riemannian manifold - Wikipedia

    en.wikipedia.org/wiki/Pseudo-Riemannian_manifold

    A principal premise of general relativity is that spacetime can be modeled as a 4-dimensional Lorentzian manifold of signature (3, 1) or, equivalently, (1, 3). Unlike Riemannian manifolds with positive-definite metrics, an indefinite signature allows tangent vectors to be classified into timelike, null or spacelike.

  6. Quizlet - Wikipedia

    en.wikipedia.org/wiki/Quizlet

    Also in 2016, Quizlet launched "Quizlet Live", a real-time online matching game where teams compete to answer all 12 questions correctly without an incorrect answer along the way. [15] In 2017, Quizlet created a premium offering called "Quizlet Go" (later renamed "Quizlet Plus"), with additional features available for paid subscribers.

  7. Signature (topology) - Wikipedia

    en.wikipedia.org/wiki/Signature_(topology)

    In the field of topology, the signature is an integer invariant which is defined for an oriented manifold M of dimension divisible by four. This invariant of a manifold has been studied in detail, starting with Rokhlin's theorem for 4-manifolds, and Hirzebruch signature theorem .

  8. Signature matrix - Wikipedia

    en.wikipedia.org/wiki/Signature_matrix

    In mathematics, a signature matrix is a diagonal matrix whose diagonal elements are plus or minus 1, that is, any matrix of the form: [1] = ...

  9. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.