Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 361]
Code Context
                $n = array_keys($lista,$lecture["Lecture"]["id"]);

                if($n[0]-1 == 0){
$playlist	=	array(
	"Playlist" => array(
	"id" => "5",
	"name" => "Geometría",
	"slug" => "geometria",
	"number" => "3",
	"description" => "Rama que se dedica al estudio de las figuras geometrícas en el plano",
	"lateral" => "1",
	"image" => "sO02HO_HPDM",
	"index" => "0"
),
	"Lecture" => array(
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array()
),
	"Chapter" => array(
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array()
)
)
$video	=	array(
	"Video" => array(
	"id" => "1875",
	"name" => "Hallar el ÁREA TOTAL de un CONO ",
	"youtube" => "iWnLNGNh49o",
	"slug" => "hallar-el-area-total-de-un-cono",
	"date" => "2017-06-01 10:58:31",
	"mp4" => "",
	"flv" => "",
	"exercise" => "",
	"words" => "area de un cono,cone´s area,superficie,area of a cone,superficie de un cono,formula,fórmula,calcular,hallar,find,finding,solving,geometry,geometria,matematicas,mate,math,jose andalon,math2me,m2m,k12,k-12,mm,education,educacion,Secondary School (School Category),mathematics,edu,secundaria,primaria,preparatoria,universidad,ingreso,examen"
),
	"Lecture" => array()
)
$time_start	=	1500669619.84
$vID	=	"1875"
$params_p	=	array(
	"conditions" => array(
	"Playlist.lateral" => "1"
),
	"order" => array(
	"Playlist.number ASC"
)
)
$playlists	=	array(
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
)
)
$lecture	=	false
$chapter_video	=	null
$positions	=	array(
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
)
)
$indexP	=	array(
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
)
)
$id	=	"5"
$title	=	"Hallar el ÁREA TOTAL de un CONO  @ math2me.com"
$params_videos_s	=	array(
	"limit" => "4",
	"order" => "Lecture.id DESC",
	"conditions" => array(
	"Lecture.playlist_id" => "5"
)
)
$videos_s	=	array(
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
)
)
$params1	=	array(
	"conditions" => array(
	"Lecture.playlist_id" => "5"
),
	"order" => array(
	"Lecture.number ASC"
)
)
$params	=	array(
	"conditions" => array(
	"Chapter.playlist_id" => "5"
),
	"order" => array(
	"Chapter.number ASC"
)
)
$videos	=	array(
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
	array(
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),
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),
	array(
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),
	array(
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	"Video" => array(),
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),
	array(
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	"Video" => array(),
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),
	array(
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	"Playlist" => array(),
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	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
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	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
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	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
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	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
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	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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),
	array(
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	"Curriculum" => array(),
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	"Video" => array(),
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),
	array(
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	"Curriculum" => array(),
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	"Video" => array(),
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),
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	"date" => "2016-02-28 17:52:19",
	"mp4" => "https://www.dropbox.com/s/mayqap3w6nwk1gg/Per%C3%ADmetro%20y%20%C3%A1rea%20de%20pol%C3%ADgonos%20-%20HD.mp4?dl=1",
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$n	=	array()
PlaylistController::video() - APP/Controller/PlaylistController.php, line 361
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 364]
Code Context
                    $anterior = null;
                }else{
                    $anterior =$lista[$n[0]-1];
$playlist	=	array(
	"Playlist" => array(
	"id" => "5",
	"name" => "Geometría",
	"slug" => "geometria",
	"number" => "3",
	"description" => "Rama que se dedica al estudio de las figuras geometrícas en el plano",
	"lateral" => "1",
	"image" => "sO02HO_HPDM",
	"index" => "0"
),
	"Lecture" => array(
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)
)
$video	=	array(
	"Video" => array(
	"id" => "1875",
	"name" => "Hallar el ÁREA TOTAL de un CONO ",
	"youtube" => "iWnLNGNh49o",
	"slug" => "hallar-el-area-total-de-un-cono",
	"date" => "2017-06-01 10:58:31",
	"mp4" => "",
	"flv" => "",
	"exercise" => "",
	"words" => "area de un cono,cone´s area,superficie,area of a cone,superficie de un cono,formula,fórmula,calcular,hallar,find,finding,solving,geometry,geometria,matematicas,mate,math,jose andalon,math2me,m2m,k12,k-12,mm,education,educacion,Secondary School (School Category),mathematics,edu,secundaria,primaria,preparatoria,universidad,ingreso,examen"
),
	"Lecture" => array()
)
$time_start	=	1500669619.84
$vID	=	"1875"
$params_p	=	array(
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),
	"order" => array(
	"Playlist.number ASC"
)
)
$playlists	=	array(
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),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
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),
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),
	array(
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),
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),
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),
	array(
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
	array(
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	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
)
)
$lecture	=	false
$chapter_video	=	null
$positions	=	array(
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
)
)
$indexP	=	array(
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
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),
	array(
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),
	array(
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	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
)
)
$id	=	"5"
$title	=	"Hallar el ÁREA TOTAL de un CONO  @ math2me.com"
$params_videos_s	=	array(
	"limit" => "4",
	"order" => "Lecture.id DESC",
	"conditions" => array(
	"Lecture.playlist_id" => "5"
)
)
$videos_s	=	array(
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
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	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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),
	array(
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	"Curriculum" => array(),
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),
	array(
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	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
)
)
$params1	=	array(
	"conditions" => array(
	"Lecture.playlist_id" => "5"
),
	"order" => array(
	"Lecture.number ASC"
)
)
$params	=	array(
	"conditions" => array(
	"Chapter.playlist_id" => "5"
),
	"order" => array(
	"Chapter.number ASC"
)
)
$videos	=	array(
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
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	"Playlist" => array(),
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	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
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$n	=	array()
PlaylistController::video() - APP/Controller/PlaylistController.php, line 364
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  -1 [APP/Controller/PlaylistController.php, line 364]
Code Context
                    $anterior = null;
                }else{
                    $anterior =$lista[$n[0]-1];
$playlist	=	array(
	"Playlist" => array(
	"id" => "5",
	"name" => "Geometría",
	"slug" => "geometria",
	"number" => "3",
	"description" => "Rama que se dedica al estudio de las figuras geometrícas en el plano",
	"lateral" => "1",
	"image" => "sO02HO_HPDM",
	"index" => "0"
),
	"Lecture" => array(
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
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),
	"Chapter" => array(
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array()
)
)
$video	=	array(
	"Video" => array(
	"id" => "1875",
	"name" => "Hallar el ÁREA TOTAL de un CONO ",
	"youtube" => "iWnLNGNh49o",
	"slug" => "hallar-el-area-total-de-un-cono",
	"date" => "2017-06-01 10:58:31",
	"mp4" => "",
	"flv" => "",
	"exercise" => "",
	"words" => "area de un cono,cone´s area,superficie,area of a cone,superficie de un cono,formula,fórmula,calcular,hallar,find,finding,solving,geometry,geometria,matematicas,mate,math,jose andalon,math2me,m2m,k12,k-12,mm,education,educacion,Secondary School (School Category),mathematics,edu,secundaria,primaria,preparatoria,universidad,ingreso,examen"
),
	"Lecture" => array()
)
$time_start	=	1500669619.84
$vID	=	"1875"
$params_p	=	array(
	"conditions" => array(
	"Playlist.lateral" => "1"
),
	"order" => array(
	"Playlist.number ASC"
)
)
$playlists	=	array(
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
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),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
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),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
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),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
)
)
$lecture	=	false
$chapter_video	=	null
$positions	=	array(
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
)
)
$indexP	=	array(
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
)
)
$id	=	"5"
$title	=	"Hallar el ÁREA TOTAL de un CONO  @ math2me.com"
$params_videos_s	=	array(
	"limit" => "4",
	"order" => "Lecture.id DESC",
	"conditions" => array(
	"Lecture.playlist_id" => "5"
)
)
$videos_s	=	array(
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
)
)
$params1	=	array(
	"conditions" => array(
	"Lecture.playlist_id" => "5"
),
	"order" => array(
	"Lecture.number ASC"
)
)
$params	=	array(
	"conditions" => array(
	"Chapter.playlist_id" => "5"
),
	"order" => array(
	"Chapter.number ASC"
)
)
$videos	=	array(
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
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	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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),
	array(
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	"Curriculum" => array(),
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	"Video" => array(),
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),
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),
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),
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	array(
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	array(
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	array(
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),
	array(
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),
	array(
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),
	array(
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),
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),
	"Lecture" => array(
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	"date" => "2016-02-28 17:52:19",
	"mp4" => "https://www.dropbox.com/s/mayqap3w6nwk1gg/Per%C3%ADmetro%20y%20%C3%A1rea%20de%20pol%C3%ADgonos%20-%20HD.mp4?dl=1",
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$n	=	array()
PlaylistController::video() - APP/Controller/PlaylistController.php, line 364
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 366]
Code Context
                    $anterior =$lista[$n[0]-1];
                }
                if($n[0]+1 > count($lista)){
$playlist	=	array(
	"Playlist" => array(
	"id" => "5",
	"name" => "Geometría",
	"slug" => "geometria",
	"number" => "3",
	"description" => "Rama que se dedica al estudio de las figuras geometrícas en el plano",
	"lateral" => "1",
	"image" => "sO02HO_HPDM",
	"index" => "0"
),
	"Lecture" => array(
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)
)
$video	=	array(
	"Video" => array(
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	"name" => "Hallar el ÁREA TOTAL de un CONO ",
	"youtube" => "iWnLNGNh49o",
	"slug" => "hallar-el-area-total-de-un-cono",
	"date" => "2017-06-01 10:58:31",
	"mp4" => "",
	"flv" => "",
	"exercise" => "",
	"words" => "area de un cono,cone´s area,superficie,area of a cone,superficie de un cono,formula,fórmula,calcular,hallar,find,finding,solving,geometry,geometria,matematicas,mate,math,jose andalon,math2me,m2m,k12,k-12,mm,education,educacion,Secondary School (School Category),mathematics,edu,secundaria,primaria,preparatoria,universidad,ingreso,examen"
),
	"Lecture" => array()
)
$time_start	=	1500669619.84
$vID	=	"1875"
$params_p	=	array(
	"conditions" => array(
	"Playlist.lateral" => "1"
),
	"order" => array(
	"Playlist.number ASC"
)
)
$playlists	=	array(
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),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
	array(
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	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
)
)
$lecture	=	false
$chapter_video	=	null
$positions	=	array(
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	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
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),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
)
)
$indexP	=	array(
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
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),
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),
	array(
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	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
)
)
$id	=	"5"
$title	=	"Hallar el ÁREA TOTAL de un CONO  @ math2me.com"
$params_videos_s	=	array(
	"limit" => "4",
	"order" => "Lecture.id DESC",
	"conditions" => array(
	"Lecture.playlist_id" => "5"
)
)
$videos_s	=	array(
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
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	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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),
	array(
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	"Playlist" => array(),
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),
	array(
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	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
)
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)
$n	=	array()
$anterior	=	null
PlaylistController::video() - APP/Controller/PlaylistController.php, line 366
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 369]
Code Context
                    $siguiente = null;
                }else{
                    $siguiente = $lista[$n[0]+1];
$playlist	=	array(
	"Playlist" => array(
	"id" => "5",
	"name" => "Geometría",
	"slug" => "geometria",
	"number" => "3",
	"description" => "Rama que se dedica al estudio de las figuras geometrícas en el plano",
	"lateral" => "1",
	"image" => "sO02HO_HPDM",
	"index" => "0"
),
	"Lecture" => array(
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
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	array(),
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),
	"Chapter" => array(
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array(),
	array()
)
)
$video	=	array(
	"Video" => array(
	"id" => "1875",
	"name" => "Hallar el ÁREA TOTAL de un CONO ",
	"youtube" => "iWnLNGNh49o",
	"slug" => "hallar-el-area-total-de-un-cono",
	"date" => "2017-06-01 10:58:31",
	"mp4" => "",
	"flv" => "",
	"exercise" => "",
	"words" => "area de un cono,cone´s area,superficie,area of a cone,superficie de un cono,formula,fórmula,calcular,hallar,find,finding,solving,geometry,geometria,matematicas,mate,math,jose andalon,math2me,m2m,k12,k-12,mm,education,educacion,Secondary School (School Category),mathematics,edu,secundaria,primaria,preparatoria,universidad,ingreso,examen"
),
	"Lecture" => array()
)
$time_start	=	1500669619.84
$vID	=	"1875"
$params_p	=	array(
	"conditions" => array(
	"Playlist.lateral" => "1"
),
	"order" => array(
	"Playlist.number ASC"
)
)
$playlists	=	array(
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
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),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
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),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
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),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
)
)
$lecture	=	false
$chapter_video	=	null
$positions	=	array(
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
),
	array(
	"Position" => array(),
	"Star" => array()
)
)
$indexP	=	array(
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
),
	array(
	"Playlist" => array(),
	"Lecture" => array(),
	"Chapter" => array()
)
)
$id	=	"5"
$title	=	"Hallar el ÁREA TOTAL de un CONO  @ math2me.com"
$params_videos_s	=	array(
	"limit" => "4",
	"order" => "Lecture.id DESC",
	"conditions" => array(
	"Lecture.playlist_id" => "5"
)
)
$videos_s	=	array(
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
)
)
$params1	=	array(
	"conditions" => array(
	"Lecture.playlist_id" => "5"
),
	"order" => array(
	"Lecture.number ASC"
)
)
$params	=	array(
	"conditions" => array(
	"Chapter.playlist_id" => "5"
),
	"order" => array(
	"Chapter.number ASC"
)
)
$videos	=	array(
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
	"Subject" => array()
),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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),
	array(
	"Lecture" => array(),
	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
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	"Video" => array(),
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),
	array(
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),
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),
	array(
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),
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),
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),
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	array(
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	array(
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	array(
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),
	array(
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),
	array(
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	"Playlist" => array(),
	"Chapter" => array(),
	"Curriculum" => array(),
	"Level" => array(),
	"Video" => array(),
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PlaylistController::video() - APP/Controller/PlaylistController.php, line 369
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

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Hallar el ÁREA TOTAL de un CONO [

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include - APP/View/Playlist/video-menu.ctp, line 382
View::_render() - CORE/Cake/View/View.php, line 598
View::render() - CORE/Cake/View/View.php, line 365
Controller::render() - CORE/Cake/Controller/Controller.php, line 899
PlaylistController::video() - APP/Controller/PlaylistController.php, line 399
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

/182]

---

Geometría

I. Cuerpos geométricos

• 1. Cuerpos geométricos │ ejercicios

II. Ángulos entre rectas

• 2. Concepto de geometría
• 3. Concepto de ángulo
• 4. Segmento recta y una recta│ejercicio 1
• 5. Líneas paralelas y perpendiculares│ej 1
• 6. Clasificación de ángulos│según su medida
• 7. Clasificación de ángulos│según su relación
• 8. Ángulos en rectas con ecuaciones│ej 1
• 9. Ángulos en rectas con ecuaciones│ej 2
• 10. Ángulos en rectas con ecuaciones│ej 3
• 11. Ángulos opuestos por el vértice│ejercicio 1
• 12. Ángulos entre paralelas y una secante
• 13. Ángulos entre paralelas y una secante│ej 1
• 14. Ángulos entre líneas paralelas con ec.│ej 1
• 15. Ángulos entre líneas paralelas con ec.│ej 2
• 16. Ángulos entre líneas paralelas con ec.│compilado
• 17. Ángulos entre paralelas y un triángulo
• 18. Ángulos interiores de un paralelogramo│ejercicio 1
• 19. Ángulo agudo de referencia en el plano cartesiano
• 20. ÁNGULOS entre LÍNEAS PARALELAS con ecuaciones │ ejercicio 1

III. Conversiones de ángulos

• 21. Convertir grados mins. y segs. a grados│ej 1
• 22. Convertir grados mins. y segs. a grados│ej 2
• 23. Convertir grados con min. y seg.│compilado 1
• 24. Convertir grados con min. y seg.│compilado 2
• 25. Complemento de un ángulo│ejercicio 1
• 26. Complemento de un ángulo con min y segs│ej 1
• 27. Complemento de un ángulo con min y segs│ej 2
• 28. Concepto de grado y radian
• 29. Convertir grados a radianes│ejercicio 1
• 30. Convertir radianes a grados│ejercicio 2
• 31. Convertir radianes a grados│ejercicio 3
• 32. Convertir radianes a grados│ejercicio 4
• 33. Convertir radianes a grados con min y seg│ej 1
• 34. Convertir grados a radianes y viceversa
• 35. Radianes en el plano cartesiano│ejercicio 1
• 36. Radianes en el plano cartesiano│ejercicio 2
• 37. Radianes en una circunferencia│ejercicio 1

IV. Ángulos de un triángulo

• 38. Clasificación de triángulos│según sus lados
• 39. Clasificación de triángulos│según sus ángulos
• 40. Triángulo isósceles│ejercicio 1
• 41. Suma de ángulos interiores de un triángulo
• 42. Ángulos interiores de un triángulo│ejercicio 1
• 43. Ángulos interiores de un triángulo│ejercicio 2
• 44. Ángulos interiores de un triángulo│ejercicio 3
• 45. Ángulos int. con fracciones de un triángulo│ej 1
• 46. Suma de dos ángulos interiores igual a uno externo
• 47. Condiciones para conocer 3 lados de un triángulo

V. Puntos y rectas de un triángulo

• 48. Rectas notables de un triángulo
• 49. Puntos notables de un triángulo
• 50. Medianas de un triángulo
• 51. Bisectrices de un triángulo
• 52. Mediatrices de un triángulo
• 53. Alturas de un triángulo
• 54. Medianas de un triángulo│demostración
• 55. Bisectrices de un triángulo│demostración
• 56. Mediatrices de un triángulo│demostración
• 57. Alturas de un triángulo│demostración
• 58. Puntos notables de un triángulo equilatero
• 59. Mediatriz y la altura│triángulo escaleno
• 60. Mediatriz y la altura│triángulo equilátero
• 61. Bisectrices en un triángulo│problema 1

VI. Área de un triángulo

• 62. Área de un triángulo con base y altura│ej 1
• 63. Perímetro y área de un triángulo│fórmula de Herón
• 64. Fórmula de Herón│ejercicio 1
• 65. Fórmula de Herón│ejercicio 2
• 66. Fórmula de Herón│ejercicio 3
• 67. Área de un triángulo equilátero│dada su altura
• 68. Área de un triángulo equilátero│fórmula con su altura
• 69. Área de un triángulo equilátero│fórmula con su lado

VII. Congruencia y Semejanza de triángulos

• 70. Congruencia y semejanza de triángulos│diferencia
• 71. Triángulos congruentes│criterios
• 72. Triángulos congruentes│ejercicio 1
• 73. Triángulos congruentes│ejercicio 2
• 74. Triángulos congruentes│ejercicio 3
• 75. Triángulos semejantes│criterios
• 76. Identificar triángulos semejantes│ej 1
• 77. Identificar triángulos semejantes│ej 2
• 78. Identificar triángulos semejantes│ej 3
• 79. Triángulos semejantes│ejercicios
• 80. Triángulos semejantes│problemas
• 81. Triángulos semejantes│problema 1
• 82. Triángulos semejantes│razón entre áreas

VIII. Teorema de Tales y Teorema de Pitágoras

• 83. Teorema de Tales
• 84. Teorema de Tales│compilado
• 85. Teorema de Tales│problema 1
• 86. Teorema de Pitágoras
• 87. Teorema de pitágoras│demostración
• 88. T. de pitágoras con fracciones │ejercicios
• 89. Teorema de pitágoras con raíces
• 90. Teorema de Pitágoras │ problema 1
• 91. Teorema de pitágoras│problema 1
• 92. Teorema de pitágoras│problema 2
• 93. Teorema de pitágoras│problema 3
• 94. Teorema de pitágoras│problema 4
• 95. Teorema de pitágoras│problema 5
• 96. Teorema de pitágoras│problema 6
• 97. Teorema de pitágoras│problema 7
• 98. Teorema de pitágoras│problema 8
• 99. Teorema de pitágoras│difícil 1
• 100. Teorema de pitágoras│difícil 2
• 101. Teorema de pitágoras│compilado

IX. Polígonos

• 102. Concepto de Polígono
• 103. Concepto de Polígono│ejercicio 1
• 104. Concepto de Polígono│ejercicio 2
• 105. Concepto de Polígono│ejercicio 3
• 106. Calcular el apotema de un polígono
• 107. Polígonos regulares
• 108. Clasificación de polígonos│nombres
• 109. Clasificación de polígonos│lados
• 110. Clasificación de polígonos│cruces aristas
• 111. Polígonos convexo y concavo
• 112. Clasificación de polígonos│ejercicio 1
• 113. Suma de los ángulos interiores de un polígono
• 114. Suma de los ángulos exteriores de un polígono
• 115. Suma de los ángulos interiores de un polígono│ej 1
• 116. Suma de los ángulos interiores de un polígono│ej 2
• 117. Ángulo interior de un polígono regular│prob 1
• 118. Diagonales de un polígono│un vértice
• 119. Diagonales de un polígono│todos los vértices
• 120. Diagonales de un polígono│hallar lados
• 121. Ángulos y diagonales de un polígono
• 122. Perímetro y área de polígonos

X. Circunferencia y círculo

• 123. Circunferencia y círculo
• 124. Como calcular el perímetro de una circunferencia
• 125. Perímetro de una circunferencia│compilado
• 126. Perímetro de una circunferencia│prob 1
• 127. Perímetro de una circunferencia│prob 2
• 128. Perímetro de una circunferencia│prob 3
• 129. Perímetro y área de un círculo
• 130. Obtener por aproximación el área de un círculo
• 131. Área de un círculo│no usar Pi
• 132. Área de un círculo│dado perímetro
• 133. Perímetro y área de un círculo│compilado
• 134. Longitud de un arco de cirunferencia de N grados
• 135. Áreas de un círculo y cuadrado│ mismo perímetro
• 136. Circunferencia tangente a una recta
• 137. Polígono inscrito y circunferencia circunscrita
• 138. Polígono circunscrito y circunferencia inscrita
• 139. Razón entre ÁREAS de CÍRCULOS │ ejercicio 1

XI. Ángulos en la circunferencia

• 140. Ángulos en la circunferencia │ ángulo central
• 141. Ángulos en la circunferencia │ ángulo inscrito
• 142. Ángulos en la circunferencia │ ángulo semiinscrito
• 143. Ángulos en la circunferencia
• 144. Ángulos en la circunferencia│demostración
• 145. Ángulos en la circunferencia│consejos
• 146. Ángulos en la circunferencia│ejercicio 1
• 147. Ángulos en la circunferencia│ejercicio 2
• 148. Ángulos en la circunferencia│compilado

XII. Áreas y perímetros

• 149. Perímetro de un triángulo con álgebra
• 150. Calcular el perímetro de una circunferencia circunscrita a un triángulo
• 151. Área y perímetro de un rombo│dadas sus diagonales
• 152. Área de un trapecio
• 153. Como obtener el ÁREA de un CUBO
• 154. Área de una pirámide rectángular
• 155. Como hallar el ÁREA DE UN CILINDRO
• 156. Hallar el ÁREA TOTAL de un CONO
• 157. Superficie de un prisma triangular regular
• 158. Superficie de una esfera
• 159. Fórmula para calcular el ÁREA de un CONO │ Deducción

XIII. Área sombreada de figuras

• 160. Áreas sombreadas en figuras│ejercicio 1
• 161. Áreas sombreadas en figuras│ejercicio 2
• 162. Áreas sombreadas en figuras │ ejercicio 3
• 163. Áreas sombreadas en figuras │ ejercicio 4
• 164. Áreas sombreadas en figuras│ejercicio 5
• 165. Áreas sombreadas en figuras│ejercicio 6
• 166. Áreas sombreadas en figuras│ejercicio 7
• 167. Áreas sombreadas en figuras│ejercicio 8
• 168. Áreas sombreadas en figuras│compilado
• 169. Áreas sombreadas en figuras │ ejercicio 5

XIV. Volumen de figuras

• 170. Volumen de figuras│fórmulas
• 171. Volumen de un cono
• 172. Volumen de un cilindro
• 173. Volumen de un cilindro│cambiar radio
• 174. Volumen de figuras│compilado
• 175. Volumen de figuras│ejercicio 1
• 176. Volumen de figuras│ejercicio 2
• 177. Volumen de una pirámide
• 178. Volumen de un cilindro
• 179. Volumen de un prisma y un cubo
• 180. Volúmen de una esfera

XV. Comparación de áreas

• 181. Comparar áreas con fórmulas │ejercicio 1
• 182. Comparar áreas SIN fórmulas │ejercicio 1

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