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- Geometric_probability abstract "Problems of the following type, and their solution techniques, were first studied in the 18th century, and the general topic became known as geometric probability. (Buffon's needle) What is the chance that a needle dropped randomly onto a floor marked with equally spaced parallel lines will cross one of the lines? What is the mean length of a random chord of a unit circle? (cf. Bertrand's paradox). What is the chance that three random points in the plane form an acute (rather than obtuse) triangle? What is the mean area of the polygonal regions formed when randomly oriented lines are spread over the plane?For mathematical development see the concise monograph by Solomon.Since the late 20th century the topic has split into two topics with different emphases. Integral geometry sprang from the principle that the mathematically natural probability models are those that are invariant under certain transformation groups. This topic emphasises systematic development of formulas for calculating expected values associated with the geometric objects derived from random points, and can in part be viewed as a sophisticated branch of multivariate calculus. Stochastic geometry emphasises the random geometrical objects themselves. For instance: different models for random lines or for random tessellations of the plane; random sets formed by making points of a spatial Poisson process be (say) centers of discs.".
- Geometric_probability wikiPageExternalLink 41134124.
- Geometric_probability wikiPageID "733613".
- Geometric_probability wikiPageLength "2228".
- Geometric_probability wikiPageOutDegree "9".
- Geometric_probability wikiPageRevisionID "634784470".
- Geometric_probability wikiPageWikiLink Bertrand_paradox_(probability).
- Geometric_probability wikiPageWikiLink Bertrands_paradox_(probability).
- Geometric_probability wikiPageWikiLink Buffons_needle.
- Geometric_probability wikiPageWikiLink Category:Geometry.
- Geometric_probability wikiPageWikiLink Category:Probability_theory.
- Geometric_probability wikiPageWikiLink Integral_geometry.
- Geometric_probability wikiPageWikiLink Multivariable_calculus.
- Geometric_probability wikiPageWikiLink Multivariate_calculus.
- Geometric_probability wikiPageWikiLink Poisson_process.
- Geometric_probability wikiPageWikiLink Stochastic_geometry.
- Geometric_probability wikiPageWikiLink Wendels_theorem.
- Geometric_probability wikiPageWikiLinkText "Geometric probability".
- Geometric_probability wikiPageWikiLinkText "Geometrical Probability".
- Geometric_probability wikiPageWikiLinkText "geometric probability".
- Geometric_probability hasPhotoCollection Geometric_probability.
- Geometric_probability subject Category:Geometry.
- Geometric_probability subject Category:Probability_theory.
- Geometric_probability type Field.
- Geometric_probability comment "Problems of the following type, and their solution techniques, were first studied in the 18th century, and the general topic became known as geometric probability. (Buffon's needle) What is the chance that a needle dropped randomly onto a floor marked with equally spaced parallel lines will cross one of the lines? What is the mean length of a random chord of a unit circle? (cf. Bertrand's paradox).".
- Geometric_probability label "Geometric probability".
- Geometric_probability sameAs Probabilitate_geometriko.
- Geometric_probability sameAs Geometrinen_todennäköisyys.
- Geometric_probability sameAs Probabilidade_geométrica.
- Geometric_probability sameAs m.052535c.
- Geometric_probability sameAs Геометрична_ймовірність.
- Geometric_probability sameAs Q327164.
- Geometric_probability sameAs Q327164.
- Geometric_probability wasDerivedFrom Geometric_probability?oldid=634784470.
- Geometric_probability isPrimaryTopicOf Geometric_probability.