About: Philo line

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In geometry, the Philo line is a line segment defined from an angle and a point inside the angle as the shortest line segment through the point that has its endpoints on the two sides of the angle. Also known as the Philon line, it is named after Philo of Byzantium, a Greek writer on mechanical devices, who lived probably during the 1st or 2nd century BC. Philo used the line to double the cube; because doubling the cube cannot be done by a straightedge and compass construction, neither can constructing the Philo line.

Attributes	Values
rdf:type	television episode
rdfs:label	Recta de Filón (es) Droite de Philon (fr) Philo line (en)
rdfs:comment	En geometría, la recta de Filón se construye a partir de un ángulo y de un punto situado en su interior, y se define como el segmento más corto que pasa por el punto y que tiene sus extremos en los dos lados del ángulo. Lleva el nombre de Filón de Bizancio, un tratadista griego que escribió sobre dispositivos mecánicos, y que vivió probablemente durante el siglo I o II a. C. Usó la recta que lleva su nombre para calcular la duplicación del cubo. Es sabido que no se puede duplicar el cubo exclusivamente con regla y compás, ni tampoco construir la recta de Filón. (es) En géométrie plane, la droite de Philon est le plus court segment joignant deux demi-droites données (Ox) et (Oy) et passant par un point A donné. Cette droite porte le nom du mathématicien mécanicien Philon de Byzance qui l'aurait mise en place pour résoudre le problème de la duplication du cube. (fr) In geometry, the Philo line is a line segment defined from an angle and a point inside the angle as the shortest line segment through the point that has its endpoints on the two sides of the angle. Also known as the Philon line, it is named after Philo of Byzantium, a Greek writer on mechanical devices, who lived probably during the 1st or 2nd century BC. Philo used the line to double the cube; because doubling the cube cannot be done by a straightedge and compass construction, neither can constructing the Philo line. (en)
foaf:depiction
dcterms:subject	Euclidean plane geometry
Wikipage page ID	9350828 (xsd:integer)
Wikipage revision ID	1121180917 (xsd:integer)
Link from a Wikipage to another Wikipage	Line segment Geometry Angle Straightedge and compass construction Mathematische Annalen Philo of Byzantium Point (geometry) Stationary point Trigonometric functions Euclidean plane geometry Cube root Triangle Doubling the cube Aspect ratio Mathesis (journal) Euclidean distance Perpendicular line
Link from a Wikipage to an external page	http://doc.utwente.nl/98526/1/art_10.1007_BF02189793.pdf https://zenodo.org/record/2474460
sameAs	Philo line Philo line Philo line Philo line Philo line
dbp:wikiPageUsesTemplate	dbt:Cite_journal dbt:Mathworld dbt:Mvar dbt:R dbt:Refbegin dbt:Refend dbt:Reflist
thumbnail	wiki-commons:Special:FilePath/Philo_line_equality.svg?width=300
title	Philo Line (en)
urlname	PhiloLine (en)
has abstract	En geometría, la recta de Filón se construye a partir de un ángulo y de un punto situado en su interior, y se define como el segmento más corto que pasa por el punto y que tiene sus extremos en los dos lados del ángulo. Lleva el nombre de Filón de Bizancio, un tratadista griego que escribió sobre dispositivos mecánicos, y que vivió probablemente durante el siglo I o II a. C. Usó la recta que lleva su nombre para calcular la duplicación del cubo. Es sabido que no se puede duplicar el cubo exclusivamente con regla y compás, ni tampoco construir la recta de Filón. (es) En géométrie plane, la droite de Philon est le plus court segment joignant deux demi-droites données (Ox) et (Oy) et passant par un point A donné. Cette droite porte le nom du mathématicien mécanicien Philon de Byzance qui l'aurait mise en place pour résoudre le problème de la duplication du cube. (fr) In geometry, the Philo line is a line segment defined from an angle and a point inside the angle as the shortest line segment through the point that has its endpoints on the two sides of the angle. Also known as the Philon line, it is named after Philo of Byzantium, a Greek writer on mechanical devices, who lived probably during the 1st or 2nd century BC. Philo used the line to double the cube; because doubling the cube cannot be done by a straightedge and compass construction, neither can constructing the Philo line. (en)
gold:hypernym	Segment
prov:wasDerivedFrom	wikipedia-en:Philo_line?oldid=1121180917&ns=0
page length (characters) of wiki page	12578 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Philo_line
is Link from a Wikipage to another Wikipage of	Philo of Byzantium Doubling the cube Philon line
is Wikipage redirect of	Philon line
is foaf:primaryTopic of	wikipedia-en:Philo_line

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