dc.creator | Šrubař, Jiří | |
dc.date.accessioned | 2021-05-24T11:08:34Z | |
dc.date.available | 2021-05-24T11:08:34Z | |
dc.date.issued | 2011 | |
dc.identifier.uri | http://hdl.handle.net/20.500.11956/32894 | |
dc.description.abstract | NA' ZEV PRA' CE Prostorova' zobecneňı' vlastnostı' troju'helnı'ku AUTOR Jirˇı' Sřubarˇ SˇKOLITEL Prof. RNDr. Adolf Karger, DrSc. SˇKOLI'CI' PRACOVISŤEˇ Katedra didaktiky matematiky ABSTRAKT V pra' ci jsou popsa' ny zajı'mave' vlastnosti troju'helnı'ku, neˇktere' vsěobecneˇ zna' me', jine' me'neˇ zna' me'. Cı'lem bylo popsat analogicke' vlastnosti cťyršteňu a tyto vlastnosti doka' zat. Prˇi du˚kazech prostorovy'ch vztahu˚ jsou pouzˇity syn- teticka' i vy'pocětnı' metoda, preferovana' je ale synteticka' metoda vzhledem k jejı' na' zornosti. Pra' ce je rozdeľena do dvou cˇa' stı'. V prvnı' cˇa' sti jsou popsa' ny ty vlastnosti cťyršteňu, ktere' odpovı'dajı' pojmu˚m težˇisťeˇ a ortocentrum troju'helnı'ku. Jsou odvozeny podmı'nky pro existenci ortocentra cťyršteňu. Da' le je pro cťyršteňy bez ortocentra zaveden Mongeu˚v bod, ktery' ma' vlastnosti ortocentru odpo- vı'dajı'cı'. V druhe' cˇa' sti pra' ce jsou zkouma' ny neˇktere' dalsˇı' vlastnosti troju'helnı'ku - - Simsonova prˇı'mka, Longchampu˚v bod, kruzňice devı'ti bodu˚, Eulerova prˇı'mka, Lemoinu˚v bod, isodynamicke' body, Lemoinova osa a Brocardova osa. Jako hlavnı' vy'sledek te'to pra' ce jsou definova' ny a je doka' za' na exis- tence prostorovy'ch analogiı' uvedeny'ch vlastnostı' troju'helnı'ku - Longcham- pova bodu... | cs_CZ |
dc.description.abstract | TITLE Spatial generalizations of the properties of the triangle AUTHOR Jirˇı' Sřubarˇ SUPERVISOR Prof. RNDr. Adolf Karger, DrSc. DEPARTMENT Department of mathematics education ABSTRACT The present thesis describes various interesting properties of a triangle. The aim is to find and prove similar properties of its spatial generalization - a tetrahedron. Even though both synthetic and computational methods are used for proving spatial relations, synthetic approach is preferred whenever possible. The thesis is divided into two parts. In the first part, the properties of the tetrahedron analogous to the centroid and the orthocenter of the triangle are described. Also, conditions on the existence of the orthocenter of the tetrahedron are derived. Moreover, for tetrahedrons without an orthocenter, the so-called Monge point is introduced as its generalization. In the second part of the thesis, some further properties of the triangle are studied - - the Simson line, the de Longchamps point, the nine-point circle, the Euler line, the Lemoine point, the isodynamic points, the Lemoine axis and the Brocard axis. As the main contribution of the present thesis we define and prove the existence of spatial analogues of the above mentioned properties for the tetrahedron - the de Longchamps point, the twelve-point and... | en_US |
dc.language | Čeština | cs_CZ |
dc.language.iso | cs_CZ | |
dc.publisher | Univerzita Karlova, Matematicko-fyzikální fakulta | cs_CZ |
dc.subject | Spatial generalization | en_US |
dc.subject | triangle | en_US |
dc.subject | tetrahedron | en_US |
dc.subject | Monge point | en_US |
dc.subject | twelve-point sphere | en_US |
dc.subject | eight-point sphere | en_US |
dc.subject | Euler line | en_US |
dc.subject | Lemoine point | en_US |
dc.subject | isodynamic point | en_US |
dc.subject | Lemoine plane | en_US |
dc.subject | Brocard axis | en_US |
dc.subject | Prostorové zobecnění | cs_CZ |
dc.subject | trojúhelník | cs_CZ |
dc.subject | čtyřstěn | cs_CZ |
dc.subject | Mongeův bod | cs_CZ |
dc.subject | kulová plocha dvanácti bodů | cs_CZ |
dc.subject | kulová plocha osmi bodů | cs_CZ |
dc.subject | Eulerova přímka | cs_CZ |
dc.subject | Lemoinův bod | cs_CZ |
dc.subject | isodynamické body | cs_CZ |
dc.subject | Lemoinova rovina | cs_CZ |
dc.subject | Brocardova osa | cs_CZ |
dc.title | Prostorová zobecnění vlastností trojúhelníku | cs_CZ |
dc.type | rigorózní práce | cs_CZ |
dcterms.created | 2011 | |
dcterms.dateAccepted | 2011-01-21 | |
dc.description.department | Katedra didaktiky matematiky | cs_CZ |
dc.description.department | Department of Mathematics Education | en_US |
dc.description.faculty | Faculty of Mathematics and Physics | en_US |
dc.description.faculty | Matematicko-fyzikální fakulta | cs_CZ |
dc.identifier.repId | 96157 | |
dc.title.translated | Spatial generalizations of the properties of the triangle | en_US |
dc.identifier.aleph | 001292154 | |
thesis.degree.name | RNDr. | |
thesis.degree.level | rigorózní řízení | cs_CZ |
thesis.degree.discipline | Učitelství matematiky - deskriptivní geometrie pro střední školy | cs_CZ |
thesis.degree.discipline | Training Teachers of Mathematics and Descriptive Geometry at Higher Secondary Schools | en_US |
thesis.degree.program | Mathematics | en_US |
thesis.degree.program | Matematika | cs_CZ |
uk.thesis.type | rigorózní práce | cs_CZ |
uk.taxonomy.organization-cs | Matematicko-fyzikální fakulta::Katedra didaktiky matematiky | cs_CZ |
uk.taxonomy.organization-en | Faculty of Mathematics and Physics::Department of Mathematics Education | en_US |
uk.faculty-name.cs | Matematicko-fyzikální fakulta | cs_CZ |
uk.faculty-name.en | Faculty of Mathematics and Physics | en_US |
uk.faculty-abbr.cs | MFF | cs_CZ |
uk.degree-discipline.cs | Učitelství matematiky - deskriptivní geometrie pro střední školy | cs_CZ |
uk.degree-discipline.en | Training Teachers of Mathematics and Descriptive Geometry at Higher Secondary Schools | en_US |
uk.degree-program.cs | Matematika | cs_CZ |
uk.degree-program.en | Mathematics | en_US |
thesis.grade.cs | Uznáno | cs_CZ |
thesis.grade.en | Recognized | en_US |
uk.abstract.cs | NA' ZEV PRA' CE Prostorova' zobecneňı' vlastnostı' troju'helnı'ku AUTOR Jirˇı' Sřubarˇ SˇKOLITEL Prof. RNDr. Adolf Karger, DrSc. SˇKOLI'CI' PRACOVISŤEˇ Katedra didaktiky matematiky ABSTRAKT V pra' ci jsou popsa' ny zajı'mave' vlastnosti troju'helnı'ku, neˇktere' vsěobecneˇ zna' me', jine' me'neˇ zna' me'. Cı'lem bylo popsat analogicke' vlastnosti cťyršteňu a tyto vlastnosti doka' zat. Prˇi du˚kazech prostorovy'ch vztahu˚ jsou pouzˇity syn- teticka' i vy'pocětnı' metoda, preferovana' je ale synteticka' metoda vzhledem k jejı' na' zornosti. Pra' ce je rozdeľena do dvou cˇa' stı'. V prvnı' cˇa' sti jsou popsa' ny ty vlastnosti cťyršteňu, ktere' odpovı'dajı' pojmu˚m težˇisťeˇ a ortocentrum troju'helnı'ku. Jsou odvozeny podmı'nky pro existenci ortocentra cťyršteňu. Da' le je pro cťyršteňy bez ortocentra zaveden Mongeu˚v bod, ktery' ma' vlastnosti ortocentru odpo- vı'dajı'cı'. V druhe' cˇa' sti pra' ce jsou zkouma' ny neˇktere' dalsˇı' vlastnosti troju'helnı'ku - - Simsonova prˇı'mka, Longchampu˚v bod, kruzňice devı'ti bodu˚, Eulerova prˇı'mka, Lemoinu˚v bod, isodynamicke' body, Lemoinova osa a Brocardova osa. Jako hlavnı' vy'sledek te'to pra' ce jsou definova' ny a je doka' za' na exis- tence prostorovy'ch analogiı' uvedeny'ch vlastnostı' troju'helnı'ku - Longcham- pova bodu... | cs_CZ |
uk.abstract.en | TITLE Spatial generalizations of the properties of the triangle AUTHOR Jirˇı' Sřubarˇ SUPERVISOR Prof. RNDr. Adolf Karger, DrSc. DEPARTMENT Department of mathematics education ABSTRACT The present thesis describes various interesting properties of a triangle. The aim is to find and prove similar properties of its spatial generalization - a tetrahedron. Even though both synthetic and computational methods are used for proving spatial relations, synthetic approach is preferred whenever possible. The thesis is divided into two parts. In the first part, the properties of the tetrahedron analogous to the centroid and the orthocenter of the triangle are described. Also, conditions on the existence of the orthocenter of the tetrahedron are derived. Moreover, for tetrahedrons without an orthocenter, the so-called Monge point is introduced as its generalization. In the second part of the thesis, some further properties of the triangle are studied - - the Simson line, the de Longchamps point, the nine-point circle, the Euler line, the Lemoine point, the isodynamic points, the Lemoine axis and the Brocard axis. As the main contribution of the present thesis we define and prove the existence of spatial analogues of the above mentioned properties for the tetrahedron - the de Longchamps point, the twelve-point and... | en_US |
uk.file-availability | V | |
uk.grantor | Univerzita Karlova, Matematicko-fyzikální fakulta, Katedra didaktiky matematiky | cs_CZ |
thesis.grade.code | U | |
uk.publication-place | Praha | cs_CZ |
uk.thesis.defenceStatus | U | |
dc.identifier.lisID | 990012921540106986 | |