Meetkunde 1: verschil tussen versies

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http://unict-21.blogskine.net/node/sistelab-ing-unict-it/ sistelab ing unict it http://tropical-grupo-4.blogskine.net/node/pesce-tropicali-africano/ pesce tropicali africano http://omega-veneto-9.mygreatblogs.net/iomega-rev-esterno/ iomega rev esterno http://vendita-tissot-80.blogskine.net vendita http://femminile-seduzione-38.mygreatblogs.net/2008/09/campionato-femminile-basket/ campionato femminile basket http://clinical-genetics-43.alumblogs.net/causes-for-clinical-depression/ causes for clinical depression http://loredana-benussi-17.mygreatblogs.net/2008/08/cannata-loredana/ cannata loredana http://informa-affari-27.mygreatblogs.net/wordpress/sistema-informatico-azienda-metalmeccaniche/ sistema informatico azienda metalmeccaniche http://rivolta-77.mygreatblogs.net/wordpress/rivolta-marghera/ rivolta marghera http://statistica-grafico-17.alumblogs.net/2008/09/grafico-recenti-economia-grecia/ grafico recenti economia grecia http://traslochi-intercontinentali-1.alumblogs.net/node/traslochi-bs/ traslochi bs http://urgenza-ospedale-13.blogskine.net/node/differenza-urgenza-ed-emergenza/ differenza urgenza ed emergenza http://organismo-notificato-67.blogskine.net/node/decreto-nomina-messo-notificatore/ decreto nomina messo notificatore http://aniello-ruggiero-94.blogskine.net/2008/08/emanuele-ruggiero/ emanuele ruggiero http://meteo-73.blogskine.net/2008/08/09/giornale-meteo/ giornale meteo http://emmanuel-micheli-38.mygreatblogs.net/2008/07/san-michelino-foro-affresco/ san michelino foro affresco http://componente-automazione-53.blogskine.net/wordpress/automazione-presse/ automazione presse http://agenzia-natalia-33.alumblogs.net/blog/entry/agenzia-viaggio-sestante-roma/ agenzia viaggio sestante roma http://affittacamere-scandicci-2.blogskine.net affittacamere http://logistica-ortofrutta-65.blogskine.net logistica http://gestore-patrimoniale-15.blogskine.net/blog/entry/regime-patrimoniale-coniugi-romania/ regime patrimoniale coniugi romania http://classe-mista-54.blogskine.net/classes-de-francais/ classes de francais http://layer-16.blogskine.net layer http://madame-bouvarie-83.mygreatblogs.net/wordpress/madame-tussaud-s-londontuta/ madame tussaud s londontuta http://wireless-network-11.blogskine.net/node/mantero-network/ mantero network http://roberto-giacomelligiacomini-34.blogskine.net/wordpress/roberto-continomotore-corrente-continua/ roberto continomotore corrente continua http://nudist-contest-36.blogskine.net/2008/07/31/economia-aziendale-contesto-riferimento/ economia aziendale contesto riferimento http://sport-34.blogskine.net/2008/08/immagini-sportive/ immagini sportive http://ebert-movie-96.blogskine.net/blog/entry/free-fucking-movie/ free fucking movie http://architettura-elaboratore-46.blogskine.net/2008/09/14/architettura-campo-concentramento/ architettura campo concentramento http://maker-22.blogskine.net/2008/08/rpg-maker/ rpg maker http://running-cpanel-96.mygreatblogs.net/running-cpanel/ running cpanel http://addio-94.blogskine.net/blog/entry/scherzo-addio-al-celibato/ scherzo addio al celibato http://cartina-eindhoven-22.mygreatblogs.net/wordpress/cartina-nicotera/ cartina nicotera http://buddy-hackett-64.alumblogs.net/blog/entry/grant-hackett/ grant hackett http://attivazione-bluetooth-76.blogskine.net/node/bluetooth-gps-receiver/ bluetooth gps receiver http://voglia-pisello-76.blogskine.net voglia http://controllo-flotta-81.mygreatblogs.net/node/controllore-logica-programmata/ controllore logica programmata http://trasmettitori-wireless-37.mygreatblogs.net trasmettitori http://antispam-solution-80.mygreatblogs.net/wordpress/web-analytics-solution/ web analytics solution http://misty-parks-47.mygreatblogs.net/2008/09/04/england-parks/ england parks http://piattaforma-logistica-56.blogskine.net/2008/08/21/trasporto-merce-logistica/ trasporto merce logistica http://camel-25.mygreatblogs.net/wordpress/camel-infisso/ camel infisso http://sorella-78.mygreatblogs.net/blog/entry/sorella-farfallina-privato-gratis/ sorella farfallina privato gratis http://video-11.alumblogs.net/wordpress/video-addio-al-nubilato/ video addio al nubilato http://scaglia-loredana-86.alumblogs.net/node/loredana-lecciso-xxx/ loredana lecciso xxx http://susan-29.alumblogs.net/blog/entry/swedish-body-builder-susanna/ swedish body builder susanna http://double-glass-85.alumblogs.net/2008/07/matura-double-penetration/ matura double penetration http://divise-calcio-86.mygreatblogs.net/node/lione-calcio/ lione calcio http://attrezzatura-giardinaggio-4.blogskine.net/2008/09/attrezzatura-equitazione-testiere/ attrezzatura equitazione testiere
http://unict-21.blogskine.net/node/sistelab-ing-unict-it/ sistelab ing unict it http://tropical-grupo-4.blogskine.net/node/pesce-tropicali-africano/ pesce tropicali africano http://omega-veneto-9.mygreatblogs.net/iomega-rev-esterno/ iomega rev esterno http://vendita-tissot-80.blogskine.net vendita http://femminile-seduzione-38.mygreatblogs.net/2008/09/campionato-femminile-basket/ campionato femminile basket http://clinical-genetics-43.alumblogs.net/causes-for-clinical-depression/ causes for clinical depression http://loredana-benussi-17.mygreatblogs.net/2008/08/cannata-loredana/ cannata loredana http://informa-affari-27.mygreatblogs.net/wordpress/sistema-informatico-azienda-metalmeccaniche/ sistema informatico azienda metalmeccaniche http://rivolta-77.mygreatblogs.net/wordpress/rivolta-marghera/ rivolta marghera http://statistica-grafico-17.alumblogs.net/2008/09/grafico-recenti-economia-grecia/ grafico recenti economia grecia http://traslochi-intercontinentali-1.alumblogs.net/node/traslochi-bs/ traslochi bs http://urgenza-ospedale-13.blogskine.net/node/differenza-urgenza-ed-emergenza/ differenza urgenza ed emergenza http://organismo-notificato-67.blogskine.net/node/decreto-nomina-messo-notificatore/ decreto nomina messo notificatore http://aniello-ruggiero-94.blogskine.net/2008/08/emanuele-ruggiero/ emanuele ruggiero http://meteo-73.blogskine.net/2008/08/09/giornale-meteo/ giornale meteo http://emmanuel-micheli-38.mygreatblogs.net/2008/07/san-michelino-foro-affresco/ san michelino foro affresco http://componente-automazione-53.blogskine.net/wordpress/automazione-presse/ automazione presse http://agenzia-natalia-33.alumblogs.net/blog/entry/agenzia-viaggio-sestante-roma/ agenzia viaggio sestante roma http://affittacamere-scandicci-2.blogskine.net affittacamere http://logistica-ortofrutta-65.blogskine.net logistica http://gestore-patrimoniale-15.blogskine.net/blog/entry/regime-patrimoniale-coniugi-romania/ regime patrimoniale coniugi romania http://classe-mista-54.blogskine.net/classes-de-francais/ classes de francais http://layer-16.blogskine.net layer http://madame-bouvarie-83.mygreatblogs.net/wordpress/madame-tussaud-s-londontuta/ madame tussaud s londontuta http://wireless-network-11.blogskine.net/node/mantero-network/ mantero network http://roberto-giacomelligiacomini-34.blogskine.net/wordpress/roberto-continomotore-corrente-continua/ roberto continomotore corrente continua http://nudist-contest-36.blogskine.net/2008/07/31/economia-aziendale-contesto-riferimento/ economia aziendale contesto riferimento http://sport-34.blogskine.net/2008/08/immagini-sportive/ immagini sportive http://ebert-movie-96.blogskine.net/blog/entry/free-fucking-movie/ free fucking movie http://architettura-elaboratore-46.blogskine.net/2008/09/14/architettura-campo-concentramento/ architettura campo concentramento http://maker-22.blogskine.net/2008/08/rpg-maker/ rpg maker http://running-cpanel-96.mygreatblogs.net/running-cpanel/ running cpanel http://addio-94.blogskine.net/blog/entry/scherzo-addio-al-celibato/ scherzo addio al celibato http://cartina-eindhoven-22.mygreatblogs.net/wordpress/cartina-nicotera/ cartina nicotera http://buddy-hackett-64.alumblogs.net/blog/entry/grant-hackett/ grant hackett http://attivazione-bluetooth-76.blogskine.net/node/bluetooth-gps-receiver/ bluetooth gps receiver http://voglia-pisello-76.blogskine.net voglia http://controllo-flotta-81.mygreatblogs.net/node/controllore-logica-programmata/ controllore logica programmata http://trasmettitori-wireless-37.mygreatblogs.net trasmettitori http://antispam-solution-80.mygreatblogs.net/wordpress/web-analytics-solution/ web analytics solution http://misty-parks-47.mygreatblogs.net/2008/09/04/england-parks/ england parks http://piattaforma-logistica-56.blogskine.net/2008/08/21/trasporto-merce-logistica/ trasporto merce logistica http://camel-25.mygreatblogs.net/wordpress/camel-infisso/ camel infisso http://sorella-78.mygreatblogs.net/blog/entry/sorella-farfallina-privato-gratis/ sorella farfallina privato gratis http://video-11.alumblogs.net/wordpress/video-addio-al-nubilato/ video addio al nubilato http://scaglia-loredana-86.alumblogs.net/node/loredana-lecciso-xxx/ loredana lecciso xxx http://susan-29.alumblogs.net/blog/entry/swedish-body-builder-susanna/ swedish body builder susanna http://double-glass-85.alumblogs.net/2008/07/matura-double-penetration/ matura double penetration http://divise-calcio-86.mygreatblogs.net/node/lione-calcio/ lione calcio http://attrezzatura-giardinaggio-4.blogskine.net/2008/09/attrezzatura-equitazione-testiere/ attrezzatura equitazione testiere


== Theorievragen ==
http://postura-definizione-41.alumblogs.net/wordpress/definizione-di-conguaglio/ definizione di conguaglio http://chueca-61.mygreatblogs.net/blog/entry/chueca-madrid-hotel/ chueca madrid hotel http://dessert-recipes-24.alumblogs.net dessert http://arrivare-lanciano-32.alumblogs.net/blog/entry/porto-ercole-arrivare/ porto ercole arrivare http://beati-santo-61.alumblogs.net/node/santo-rosario-mese-maggio/ santo rosario mese maggio http://uniform-89.alumblogs.net/moto-uniforme-accellerator/ moto uniforme accellerator http://close-99.alumblogs.net/node/rubbermaid-closet-system/ rubbermaid closet system http://grigio-argento-40.mygreatblogs.net/2008/09/09/creazione-in-argento/ creazione in argento http://digestione-difficile-21.alumblogs.net/blog/entry/un-ragazzo-difficile/ un ragazzo difficile http://bergamo-38.blogskine.net/blog/entry/bed-and-breakfast-bergamo/ bed and breakfast bergamo http://motorsport-28.alumblogs.net/2008/08/golf-rallye-motorsport/ golf rallye motorsport http://sevenseas-hooker-60.mygreatblogs.net/node/viaggio-mullen-hooker-co/ viaggio mullen hooker co http://invio-64.alumblogs.net/sms-pronto-gratis-invio/ sms pronto gratis invio http://martino-ginepro-72.mygreatblogs.net/node/martino-cervo/ martino cervo http://modus-solution-16.alumblogs.net/blog/entry/modus-ponens-inserimento/ modus ponens inserimento http://sissi-bouledogue-93.mygreatblogs.net/blog/entry/bouledogue-francese/ bouledogue francese http://interactive-phisic-64.alumblogs.net/wordpress/virtual-earth-interactive-sdk/ virtual earth interactive sdk http://modulistica-privacy-46.alumblogs.net/2008/09/privacy-scuola/ privacy scuola http://danno-patrimoniale-55.mygreatblogs.net/wordpress/addebito-danno/ addebito danno http://varian-microeconomia-38.blogskine.net/blog/entry/economia-benessere-politica-microeconomia/ economia benessere politica microeconomia http://logos-olivetti-82.mygreatblogs.net/blog/entry/fotocopiatrice-olivetti/ fotocopiatrice olivetti http://dondolo-terrazzo-92.alumblogs.net/giocattolo-cavallo-dondolo/ giocattolo cavallo dondolo http://salto-valenta-58.blogskine.net/2008/09/01/equitazione-salto-ostacoli-pony/ equitazione salto ostacoli pony http://estensione-83.mygreatblogs.net/blog/entry/estensione-buco-dell-ozono/ estensione buco dell ozono http://mangime-hills-38.alumblogs.net/2008/08/dieta-beverly-hills/ dieta beverly hills http://visconti-44.blogskine.net/node/gudo-visconti/ gudo visconti http://ghiaccio-sintetico-41.mygreatblogs.net/marmo-sintetico/ marmo sintetico http://programma-tesmed-20.alumblogs.net programma http://tsukiko-amano-73.blogskine.net/node/rotoli-asciugamano/ rotoli asciugamano http://maltese-33.mygreatblogs.net/wordpress/colto-maltese/ colto maltese http://italia-76.alumblogs.net/wordpress/traduzione-italiano-greco/ traduzione italiano greco http://topless-boxing-43.alumblogs.net/wordpress/female-boxing/ female boxing http://cerchiamo-bagnino-41.alumblogs.net/cerchiamo-madrelingua-russa/ cerchiamo madrelingua russa http://coltello-tanto-71.alumblogs.net/wordpress/ne-tanto-meno/ ne tanto meno http://engher-11.alumblogs.net/node/provino-eva-engher/ provino eva engher http://studio-grafico-59.mygreatblogs.net/node/annuncio-lavoro-grafico-lazio/ annuncio lavoro grafico lazio http://tipologia-urbane-97.mygreatblogs.net/blog/entry/cosa-servono-tipologia-letterarie/ cosa servono tipologia letterarie http://capannone-mozzate-44.blogskine.net/2008/08/capannone-gallarate/ capannone gallarate http://rivolta-77.mygreatblogs.net rivolta http://alessia-olive-63.blogskine.net/2008/08/09/ww-meteogiornale-itmeteolive/ ww meteogiornale itmeteolive http://elenoire-lacroix-44.mygreatblogs.net/node/elenoire-versus/ elenoire versus http://bistrot-pergine-52.alumblogs.net/blog/entry/numberone-paradiso-pergine/ numberone paradiso pergine http://university-graduate-84.alumblogs.net/2008/09/01/london-metropolitan-university/ london metropolitan university http://sconto-telefonata-21.alumblogs.net/node/telefonata-bestemmia-napoli/ telefonata bestemmia napoli http://divani-relax-2.mygreatblogs.net/wordpress/divani-in-bianco/ divani in bianco http://mangime-hills-38.alumblogs.net/2008/08/chianti-hills-farmhouse/ chianti hills farmhouse http://europa-68.alumblogs.net/tomtom-one-xl-europa/ tomtom one xl europa http://succo-centrifugati-67.alumblogs.net succo http://lavello-acciaio-51.mygreatblogs.net/wordpress/stufa-acciaio/ stufa acciaio http://gentilini-luciana-19.blogskine.net/2008/08/luciana-salazar-escote/ luciana salazar escote
Een lijst met theorievragen die Professor Dillen reeds gesteld heeft, afkomstig uit de examenvragenbundel van Cudi.
 
=== Euclidische meetkunde ===
 
# Je mag zeker een vraag verwachten waarbij je ofwel de oriëntatiebewarende ofwel de oriëntatieomkerende isometrieën van <math>\mathbb{E}^2</math> of <math>\mathbb{E}^3</math> moet classificeren.
# Definieer rotatie in <math>\mathbb{E}^2</math> en <math>\mathbb{E}^3</math>.
# Definieer spiegeling en bewijs dat het een isometrie is.
#
#* Definieer schroefbeweging en rotatie in <math>\mathbb{E}^3</math> en geef uitgebreid commentaar.
#* Bewijs dan dat elke oriëntatiebewarende isometrie van <math>\mathbb{E}^3</math> een translatie of schroefbeweging is.
# Zij <math>F : \mathbb{E}^n \to \mathbb{E}^n</math> een willekeurige afbeelding. Bewijs dat F een isometrie is als en slechts als d(F(p), F(q)) = d(p,q) voor alle <math>p,q \in \mathbb{E}^n</math>.
# Bewijs de volgende stelling: Zij F een isometrie. Dan bestaat er juist één isometrie G en juist één translatie <math>t_b</math> zodat
#* <math>F = t_b \circ G</math>
#* <math>V(G) \neq \emptyset</math>
#* <math>G_* b = b</math>
#: Bovendien is dan ook <math>t_b \circ G =G \circ t_b</math> en V(G) is een affiene deelruimte in de richting van <math>\ker (F_* - I)</math>.
 
=== Krommen ===
 
# Geef het Frenetstelsel voor vlakke krommen en formuleer de congruentiestelling. Vergelijk het Frenetstelsel van congruente krommen met dat van booglengtegeparamatriseerde krommen.
# Bewijs dat een reguliere kromme in <math>\mathbb{E}^3</math> een vlakke kromme is als en slechts als de torsie 0 is.
#
#* In <math>\mathbb{E}^2</math>. Toon aan dat de kromming de kromme volledig bepaalt.
#* Definieer gesloten krommen en de rotatie-index en verklaar hoe de rotatie-index bepaald kan worden uit de kromming.
#
#* Definieer de cirkelschroeflijn en de cilinderschroeflijn en verklaar de naamgeving.
#* Geef de nodige en voldoende voorwaarden voor de kromming en torsie zodat een reguliere kromme een cilinderschroeflijn is.
#
#* Definieer het Frenet-referentiestelsel voor ruimtekrommen en bewijs de formules van Frenet.
#* Formuleer en bewijs de congruentiestelling voor ruimtekrommen.
# Formuleer en bewijs de congruentiestelling voor booglengtegeparametriseerde vlakke krommen.
# Rechten realiseren de kortste afstand tussen twee punten. Behandel uitvoerig.


== Tussentijdse toetsen ==
== Tussentijdse toetsen ==

Versie van 27 sep 2008 22:21

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Tussentijdse toetsen

2006-04-??

  1. Geef een basis voor de richting van de volgende affiene deelruimte van 𝔸4:
    x1−x3−x4=−1
    x1+x2−2x3=1
    x2−x3+x4=2
    x1+3x2−4x3+2x4=5
  2. Zij S een niet-lege deelverzameling van 𝔸n. Toon aan: S is een affiene deelruimte van 𝔸n als en slechts als voor elk tweetal punten p, q van S de verbindingsrechte pq tot S behoort.
  3. Zij b, c twee vaste punten in 𝔸2 en L een vaste rechte die bc snijdt in p. Toon aan dat de zwaartepunten van de driehoeken abc, waarbij a varieert op L \ {p}, steeds tot een vaste rechte behoren. Doe dit
    • analytisch;
    • synthetisch.
    (Voor het synthetisch bewijs mag je alle eigenschappen uit de cursus en de oefenzittingen gebruiken, maar zeg er wel bij welke eigenschap je gebruikt.)
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