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  2. Volume of an n-ball - Wikipedia

    en.wikipedia.org/wiki/Volume_of_an_n-ball

    The volume of the n-ball () can be computed by integrating the volume element in spherical coordinates. The spherical coordinate system has a radial coordinate r and angular coordinates φ 1, …, φ n1, where the domain of each φ except φ n1 is [0, π), and the domain of φ n1 is [0, 2 π). The spherical volume element is:

  3. Observantism - Wikipedia

    en.wikipedia.org/wiki/Observantism

    Observantism (also called the observant movement or observant reform) [1] was a reform movement affecting most of the religious orders of the Latin Church. [2] It lasted from the mid-14th until the early-to-mid 16th century. [ 3 ]

  4. Hilbert's eighth problem - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_eighth_problem

    Hilbert's eighth problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns number theory , and in particular the Riemann hypothesis , [ 1 ] although it is also concerned with the Goldbach conjecture .

  5. Genus (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Genus_(mathematics)

    The genus of a graph is the minimal integer n such that the graph can be drawn without crossing itself on a sphere with n handles (i.e. an oriented surface of the genus n). Thus, a planar graph has genus 0, because it can be drawn on a sphere without self-crossing.

  6. Intuitionism - Wikipedia

    en.wikipedia.org/wiki/Intuitionism

    The fundamental distinguishing characteristic of intuitionism is its interpretation of what it means for a mathematical statement to be true. In Brouwer's original intuitionism, the truth of a mathematical statement is a subjective claim: a mathematical statement corresponds to a mental construction, and a mathematician can assert the truth of a statement only by verifying the validity of that ...

  7. Rule of succession - Wikipedia

    en.wikipedia.org/wiki/Rule_of_succession

    In probability theory, the rule of succession is a formula introduced in the 18th century by Pierre-Simon Laplace in the course of treating the sunrise problem. [1] The formula is still used, particularly to estimate underlying probabilities when there are few observations or events that have not been observed to occur at all in (finite) sample data.

  8. Adapted process - Wikipedia

    en.wikipedia.org/wiki/Adapted_process

    Consider a stochastic process X : [0, T] × Ω → R, and equip the real line R with its usual Borel sigma algebra generated by the open sets.. If we take the natural filtration F • X, where F t X is the σ-algebra generated by the pre-images X s1 (B) for Borel subsets B of R and times 0 ≤ s ≤ t, then X is automatically F • X-adapted.

  9. Logical intuition - Wikipedia

    en.wikipedia.org/wiki/Logical_intuition

    Logical Intuition, or mathematical intuition or rational intuition, is a series of instinctive foresight, know-how, and savviness often associated with the ability to perceive logical or mathematical truth—and the ability to solve mathematical challenges efficiently. [1]

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