About: Polar circle (geometry)     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.org associated with source document(s)
QRcode icon
http://dbpedia.org/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FPolar_circle_%28geometry%29

In geometry, the polar circle of a triangle is the circle whose center is the triangle's orthocenter and whose squared radius is where A, B, C denote both the triangle's vertices and the angle measures at those vertices, H is the orthocenter (the intersection of the triangle's altitudes), D, E, F are the feet of the altitudes from vertices A, B, C respectively, R is the triangle's circumradius (the radius of its circumscribed circle), and a, b, c are the lengths of the triangle's sides opposite vertices A, B, C respectively.

AttributesValues
rdfs:label
  • Polar circle (geometry)
rdfs:comment
  • In geometry, the polar circle of a triangle is the circle whose center is the triangle's orthocenter and whose squared radius is where A, B, C denote both the triangle's vertices and the angle measures at those vertices, H is the orthocenter (the intersection of the triangle's altitudes), D, E, F are the feet of the altitudes from vertices A, B, C respectively, R is the triangle's circumradius (the radius of its circumscribed circle), and a, b, c are the lengths of the triangle's sides opposite vertices A, B, C respectively.
sameAs
dct:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
foaf:depiction
  • External Image
foaf:isPrimaryTopicOf
thumbnail
prov:wasDerivedFrom
has abstract
  • In geometry, the polar circle of a triangle is the circle whose center is the triangle's orthocenter and whose squared radius is where A, B, C denote both the triangle's vertices and the angle measures at those vertices, H is the orthocenter (the intersection of the triangle's altitudes), D, E, F are the feet of the altitudes from vertices A, B, C respectively, R is the triangle's circumradius (the radius of its circumscribed circle), and a, b, c are the lengths of the triangle's sides opposite vertices A, B, C respectively. The first parts of the radius formula reflect the fact that the orthocenter divides the altitudes into segment pairs of equal products. The trigonometric formula for the radius shows that the polar circle has a real existence only if the triangle is obtuse, so one of its angles is obtuse and hence has a negative cosine.
http://purl.org/voc/vrank#hasRank
is Link from a Wikipage to another Wikipage of
is foaf:primaryTopic of
Faceted Search & Find service v1.17_git39 as of Aug 09 2019


Alternative Linked Data Documents: PivotViewer | iSPARQL | ODE     Content Formats:       RDF       ODATA       Microdata      About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 07.20.3235 as of Sep 1 2020, on Linux (x86_64-generic-linux-glibc25), Single-Server Edition (61 GB total memory)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2020 OpenLink Software