Matches in DBpedia 2016-04 for { <http://wikidata.dbpedia.org/resource/Q327164> ?p ?o }
Showing triples 1 to 15 of
15
with 100 triples per page.
- Q327164 subject Q5639957.
- Q327164 subject Q6436127.
- Q327164 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.".
- Q327164 wikiPageExternalLink 41134124.
- Q327164 wikiPageWikiLink Q1145117.
- Q327164 wikiPageWikiLink Q1666739.
- Q327164 wikiPageWikiLink Q1753097.
- Q327164 wikiPageWikiLink Q2035437.
- Q327164 wikiPageWikiLink Q2725319.
- Q327164 wikiPageWikiLink Q5639957.
- Q327164 wikiPageWikiLink Q6436127.
- Q327164 wikiPageWikiLink Q7982357.
- Q327164 wikiPageWikiLink Q828552.
- Q327164 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).".
- Q327164 label "Geometric probability".