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?
| Attributes | Values |
|---|
| rdf:type
| |
| rdfs:label
| - Probabilitate geometriko (eu)
- Geometric probability (en)
- Probabilidade geométrica (pt)
- Геометрична ймовірність (uk)
|
| rdfs:comment
| - Геометрична ймовірність — це поняття ймовірності, що запроваджується так: Нехай — деяка підмножина прямої, площини чи простору. Випадкова подія — підмножина . Тоді ймовірність випадкової події визначається формулою: де — довжина, площа чи об'єм множин та . Це пов'язане з інтерпретацією ймовірності як міри на обраному просторі елементарних подій. В даному випадку він збігається з евклідовим простором. (uk)
- 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? (en)
- Probabilitate geometrikoa probabilitatea eta geometria uztartzen dituen arloari deritzo, geometriaren bitartez probabilitateari buruzko ebazkizunak ebatziz zein probabilitate-kalkulu eta teoriaren bitartez, objektu geometrikoen propietateak ikertuz. Adibidez, Probabilitate geometrikoa matematikako ebazkizun klasiko zenbaitetan agertzen da, XVIII. mendeko Buffonen orratz-ebazkizuna esaterako. Jolas-matematikako ebazkizunak asmatu eta ebazteko ere erabiltzen da. (eu)
- Problemas do seguinte tipo, e as técnicas para solucioná-los, foram primeiramente estudados no século XVIII, sendo a resolução do problema da agulha de Buffon, em 1777, considerada o marco inicial do tópico geral que ficou conhecido como probabilidade geométrica. No final do século XX, o tema foi dividido em dois temas com ênfases diferentes: geometria integral e . (pt)
|
| dcterms:subject
| |
| Wikipage page ID
| |
| Wikipage revision ID
| |
| Link from a Wikipage to another Wikipage
| |
| Link from a Wikipage to an external page
| |
| sameAs
| |
| dbp:wikiPageUsesTemplate
| |
| has 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. (en)
- Probabilitate geometrikoa probabilitatea eta geometria uztartzen dituen arloari deritzo, geometriaren bitartez probabilitateari buruzko ebazkizunak ebatziz zein probabilitate-kalkulu eta teoriaren bitartez, objektu geometrikoen propietateak ikertuz. Adibidez,
* geometriaren bitartez, probabilitate bat kalkulatuz: gezi bat zati bereiziak dituen itu baterantz zoriz jaurtita, zenbatekoa da zati jakin batean suertatzeko probabilitatea?
* probabilitatearen bitartez, objektu geometriko baten propietateei buruz: zirkunferentzia batetik zoriz bi puntu aukeratzen badira, zenbatekoa da bi puntuak lotzen dituen zuzenkiaren batez besteko luzera? Probabilitate geometrikoa matematikako ebazkizun klasiko zenbaitetan agertzen da, XVIII. mendeko Buffonen orratz-ebazkizuna esaterako. Jolas-matematikako ebazkizunak asmatu eta ebazteko ere erabiltzen da. (eu)
- Problemas do seguinte tipo, e as técnicas para solucioná-los, foram primeiramente estudados no século XVIII, sendo a resolução do problema da agulha de Buffon, em 1777, considerada o marco inicial do tópico geral que ficou conhecido como probabilidade geométrica.
* Agulha de Buffon: Qual é a chance de que uma agulha largada aleatoriamente em um chão marcado com linhas retas paralelas igualmente espaçadas cruze com uma das retas?
* Qual é o comprimento médio de uma corda aleatória de um círculo unitário? (cf. ).
* Qual é a chance de que três pontos aleatórios do plano formem um triângulo agudo?
* Qual é a área média das regiões poligonais formadas quando linhas retas orientadas aleatoriamente são espalhadas sobre o plano? No final do século XX, o tema foi dividido em dois temas com ênfases diferentes: geometria integral e . (pt)
- Геометрична ймовірність — це поняття ймовірності, що запроваджується так: Нехай — деяка підмножина прямої, площини чи простору. Випадкова подія — підмножина . Тоді ймовірність випадкової події визначається формулою: де — довжина, площа чи об'єм множин та . Це пов'язане з інтерпретацією ймовірності як міри на обраному просторі елементарних подій. В даному випадку він збігається з евклідовим простором. (uk)
|
| prov:wasDerivedFrom
| |
| page length (characters) of wiki page
| |
| foaf:isPrimaryTopicOf
| |
| is Link from a Wikipage to another Wikipage
of | |
| is Wikipage redirect
of | |
| is foaf:primaryTopic
of | |
![[RDF Data]](/fct/images/sw-rdf-blue.png)
![[cxml]](/fct/images/cxml_doc.png)
![[csv]](/fct/images/csv_doc.png)
![[text]](/fct/images/ntriples_doc.png)
![[turtle]](/fct/images/n3turtle_doc.png)
![[ld+json]](/fct/images/jsonld_doc.png)
![[rdf+json]](/fct/images/json_doc.png)
![[rdf+xml]](/fct/images/xml_doc.png)
![[atom+xml]](/fct/images/atom_doc.png)
![[html]](/fct/images/html_doc.png)