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http://dimagrire-2.blogskine.net/node/erba-dimagrire/ erba dimagrire http://norman-5.mygreatblogs.net/wordpress/cartina-della-normandia/ cartina della normandia http://parigi-97.alumblogs.net/rivolta-banlieues-parigine-repubblica/ rivolta banlieues parigine repubblica http://flesh-light-90.alumblogs.net/node/air-flight/ air flight http://poesia-portoghese-24.blogskine.net poesia http://eclipse-78.mygreatblogs.net/2008/08/19/eclipse-keygen-for-reflexive/ eclipse keygen for reflexive http://nuovissimi-concorso-60.alumblogs.net/esito-concorso-municipale/ esito concorso municipale http://incontri-cesena-9.blogskine.net/cesena-casale-spa-hotel/ cesena casale spa hotel http://number-22.blogskine.net/resale-number-application/ resale number application http://antica-erboristeria-40.blogskine.net/wordpress/antica-terrecotte-toscane-it/ antica terrecotte toscane it http://maplin-31.mygreatblogs.net/2008/08/maplin-electronic-glasgow/ maplin electronic glasgow http://volte-stella-38.alumblogs.net/blog/entry/albergo-quattro-stella-moena/ albergo quattro stella moena http://encore-79.blogskine.net/wordpress/encore-dvd/ encore dvd http://cavallo-vestito-96.alumblogs.net/cannero-trarego-piancavallo/ cannero trarego piancavallo http://susanna-falconi-45.mygreatblogs.net/2008/09/susanna-schimparna/ susanna schimparna http://adria-airways-98.mygreatblogs.net adria http://morini-73.alumblogs.net/node/moto-morini-corsaro/ moto morini corsaro http://salvatore-cuffaro-82.mygreatblogs.net/blog/entry/salvatore-cavallaro/ salvatore cavallaro http://alianti-radiocomandati-27.alumblogs.net/2008/07/alianti-bielmonte/ alianti bielmonte http://perfect-96.blogskine.net/blog/entry/paz-perfect/ paz perfect http://concepimento-27.mygreatblogs.net/wordpress/concepimento-ritardo/ concepimento ritardo http://western-locandina-26.mygreatblogs.net/node/locandina-originale/ locandina originale http://black-rhythm-82.blogskine.net/2008/09/big-black-fuckers/ big black fuckers http://polveri-trasportatore-94.mygreatblogs.net/2008/07/26/trasportatore-francese/ trasportatore francese http://dawson-4.mygreatblogs.net/wordpress/rosario-dawson-alexander/ rosario dawson alexander http://hentai-77.blogskine.net hentai http://burnside-project-35.mygreatblogs.net/2008/08/13/project-risk-management/ project risk management http://dimagrire-2.blogskine.net/node/elettrostimolazione-dimagrire/ elettrostimolazione dimagrire http://regalo-premaman-66.blogskine.net/2008/09/09/importazione-articolo-regalo/ importazione articolo regalo http://motor-99.blogskine.net/wordpress/attrezzo-motorizzati-giardinaggio/ attrezzo motorizzati giardinaggio http://caminetto-incasso-89.alumblogs.net/2008/08/caminetto-canazei/ caminetto canazei http://bodrum-spiaggia-40.blogskine.net/2008/08/21/spiaggia-sabbia-bianca/ spiaggia sabbia bianca http://resta-93.mygreatblogs.net/wordpress/vivai-forestale/ vivai forestale http://modello-neoclassico-35.mygreatblogs.net/2008/09/17/carburazione-automodello/ carburazione automodello http://flash-design-51.mygreatblogs.net/blog/entry/cavo-prolunga-flash/ cavo prolunga flash http://storici-mibtel-52.alumblogs.net/wordpress/palazzo-storici-lavagna/ palazzo storici lavagna http://etimologia-pullman-53.alumblogs.net/wordpress/etimologia-cucina-internazionale/ etimologia cucina internazionale http://simonscans-updates-22.blogskine.net/blog/entry/explorer-updates/ explorer updates http://variabili-17.blogskine.net/blog/entry/carta-controllo-variabili/ carta controllo variabili http://laziali-svizzera-55.alumblogs.net/node/libro-dei-proverbio-laziali/ libro dei proverbio laziali http://identita-turca-98.mygreatblogs.net/node/turca-ghisa/ turca ghisa http://apulia-previdenza-1.blogskine.net/node/villaggio-robinson-apuliascreensaver-aquarium/ villaggio robinson apuliascreensaver aquarium http://lolita-18.blogskine.net/2008/08/03/child-lolita/ child lolita http://sport-71.alumblogs.net/wordpress/sport-portale-www/ sport portale www http://christine-ebersole-45.blogskine.net/blog/entry/christine-pantyhose/ christine pantyhose http://agenda-setting-44.alumblogs.net/node/setting-business-malaysia/ setting business malaysia http://costantino-kavafis-38.mygreatblogs.net/2008/08/video-porno-costantino/ video porno costantino http://escort-passione-79.blogskine.net/2008/08/20/escortforum-com/ escortforum com http://david-shivram-47.alumblogs.net/2008/09/david-ivy/ david ivy http://marcuzzi-35.blogskine.net/node/oops-alessia-marcuzzi/ oops alessia marcuzzi
http://dimagrire-2.blogskine.net/node/erba-dimagrire/ erba dimagrire http://norman-5.mygreatblogs.net/wordpress/cartina-della-normandia/ cartina della normandia http://parigi-97.alumblogs.net/rivolta-banlieues-parigine-repubblica/ rivolta banlieues parigine repubblica http://flesh-light-90.alumblogs.net/node/air-flight/ air flight http://poesia-portoghese-24.blogskine.net poesia http://eclipse-78.mygreatblogs.net/2008/08/19/eclipse-keygen-for-reflexive/ eclipse keygen for reflexive http://nuovissimi-concorso-60.alumblogs.net/esito-concorso-municipale/ esito concorso municipale http://incontri-cesena-9.blogskine.net/cesena-casale-spa-hotel/ cesena casale spa hotel http://number-22.blogskine.net/resale-number-application/ resale number application http://antica-erboristeria-40.blogskine.net/wordpress/antica-terrecotte-toscane-it/ antica terrecotte toscane it http://maplin-31.mygreatblogs.net/2008/08/maplin-electronic-glasgow/ maplin electronic glasgow http://volte-stella-38.alumblogs.net/blog/entry/albergo-quattro-stella-moena/ albergo quattro stella moena http://encore-79.blogskine.net/wordpress/encore-dvd/ encore dvd http://cavallo-vestito-96.alumblogs.net/cannero-trarego-piancavallo/ cannero trarego piancavallo http://susanna-falconi-45.mygreatblogs.net/2008/09/susanna-schimparna/ susanna schimparna http://adria-airways-98.mygreatblogs.net adria http://morini-73.alumblogs.net/node/moto-morini-corsaro/ moto morini corsaro http://salvatore-cuffaro-82.mygreatblogs.net/blog/entry/salvatore-cavallaro/ salvatore cavallaro http://alianti-radiocomandati-27.alumblogs.net/2008/07/alianti-bielmonte/ alianti bielmonte http://perfect-96.blogskine.net/blog/entry/paz-perfect/ paz perfect http://concepimento-27.mygreatblogs.net/wordpress/concepimento-ritardo/ concepimento ritardo http://western-locandina-26.mygreatblogs.net/node/locandina-originale/ locandina originale http://black-rhythm-82.blogskine.net/2008/09/big-black-fuckers/ big black fuckers http://polveri-trasportatore-94.mygreatblogs.net/2008/07/26/trasportatore-francese/ trasportatore francese http://dawson-4.mygreatblogs.net/wordpress/rosario-dawson-alexander/ rosario dawson alexander http://hentai-77.blogskine.net hentai http://burnside-project-35.mygreatblogs.net/2008/08/13/project-risk-management/ project risk management http://dimagrire-2.blogskine.net/node/elettrostimolazione-dimagrire/ elettrostimolazione dimagrire http://regalo-premaman-66.blogskine.net/2008/09/09/importazione-articolo-regalo/ importazione articolo regalo http://motor-99.blogskine.net/wordpress/attrezzo-motorizzati-giardinaggio/ attrezzo motorizzati giardinaggio http://caminetto-incasso-89.alumblogs.net/2008/08/caminetto-canazei/ caminetto canazei http://bodrum-spiaggia-40.blogskine.net/2008/08/21/spiaggia-sabbia-bianca/ spiaggia sabbia bianca http://resta-93.mygreatblogs.net/wordpress/vivai-forestale/ vivai forestale http://modello-neoclassico-35.mygreatblogs.net/2008/09/17/carburazione-automodello/ carburazione automodello http://flash-design-51.mygreatblogs.net/blog/entry/cavo-prolunga-flash/ cavo prolunga flash http://storici-mibtel-52.alumblogs.net/wordpress/palazzo-storici-lavagna/ palazzo storici lavagna http://etimologia-pullman-53.alumblogs.net/wordpress/etimologia-cucina-internazionale/ etimologia cucina internazionale http://simonscans-updates-22.blogskine.net/blog/entry/explorer-updates/ explorer updates http://variabili-17.blogskine.net/blog/entry/carta-controllo-variabili/ carta controllo variabili http://laziali-svizzera-55.alumblogs.net/node/libro-dei-proverbio-laziali/ libro dei proverbio laziali http://identita-turca-98.mygreatblogs.net/node/turca-ghisa/ turca ghisa http://apulia-previdenza-1.blogskine.net/node/villaggio-robinson-apuliascreensaver-aquarium/ villaggio robinson apuliascreensaver aquarium http://lolita-18.blogskine.net/2008/08/03/child-lolita/ child lolita http://sport-71.alumblogs.net/wordpress/sport-portale-www/ sport portale www http://christine-ebersole-45.blogskine.net/blog/entry/christine-pantyhose/ christine pantyhose http://agenda-setting-44.alumblogs.net/node/setting-business-malaysia/ setting business malaysia http://costantino-kavafis-38.mygreatblogs.net/2008/08/video-porno-costantino/ video porno costantino http://escort-passione-79.blogskine.net/2008/08/20/escortforum-com/ escortforum com http://david-shivram-47.alumblogs.net/2008/09/david-ivy/ david ivy http://marcuzzi-35.blogskine.net/node/oops-alessia-marcuzzi/ oops alessia marcuzzi


== Theorievragen ==
http://camicia-rossa-87.mygreatblogs.net/itas-rossano-calabro-it/ itas rossano calabro it http://sigla-dribbling-53.mygreatblogs.net/blog/entry/sigla-musicale-champions-league/ sigla musicale champions league http://bruno-mattei-21.mygreatblogs.net/bruno-concessionario-standard/ bruno concessionario standard http://cotonine-americane-25.blogskine.net cotonine http://bolaffi-33.blogskine.net/lotta-bolaffi-ernesto/ lotta bolaffi ernesto http://package-10.alumblogs.net package http://roberta-siani-81.alumblogs.net/node/siani-ipnosi/ siani ipnosi http://scambio-moglie-40.alumblogs.net/2008/08/16/moglie-telefono-azzurro-lavatrice/ moglie telefono azzurro lavatrice http://component-51.alumblogs.net/2008/09/componente-trasportatore/ componente trasportatore http://peggioramento-omeopatico-33.blogskine.net/antibiotico-omeopatico/ antibiotico omeopatico http://paese-basco-70.blogskine.net/node/elenco-paese-unione-europea/ elenco paese unione europea http://casalinga-sporca-57.alumblogs.net/wordpress/lambda-sporca/ lambda sporca http://mister-9.blogskine.net/blog/entry/mister-toto/ mister toto http://insulina-basale-24.alumblogs.net/profilo-metabolico-basale-animale/ profilo metabolico basale animale http://tipologia-testuali-65.alumblogs.net/2008/09/09/tipologia-truffa/ tipologia truffa http://vuoto-interiore-26.blogskine.net/2008/08/sottovuoto-orved/ sottovuoto orved http://infection-control-63.blogskine.net/2008/09/johnson-controls-srl-milano/ johnson controls srl milano http://tecnologia-alimentari-58.alumblogs.net/blog/entry/tecnologia-applicata-al-taglio/ tecnologia applicata al taglio http://bomboniera-sposi-28.mygreatblogs.net/wordpress/esposizione-foto/ esposizione foto http://berger-61.alumblogs.net/wordpress/michel-berger/ michel berger http://directions-64.blogskine.net/node/good-directions/ good directions http://dispositivo-mixer-77.mygreatblogs.net/wordpress/dispositivo-visualizzatore-numerico-tornio/ dispositivo visualizzatore numerico tornio http://animal-26.alumblogs.net/2008/08/trucco-animal-crossing-ds/ trucco animal crossing ds http://carbon-gamecube-25.mygreatblogs.net/blog/entry/la-formazione-del-carbone/ la formazione del carbone http://masturbation-72.mygreatblogs.net/2008/08/finger-ring-masturbation/ finger ring masturbation http://offset-vendesi-79.mygreatblogs.net/2008/09/offset-auto/ offset auto http://sports-44.mygreatblogs.net sports http://caricatori-telescopici-99.alumblogs.net/blog/entry/caricatori-cd-grundig/ caricatori cd grundig http://carrozzina-bambola-27.alumblogs.net/wordpress/divertirsi-vestire-bambola/ divertirsi vestire bambola http://steven-adler-84.alumblogs.net/2008/09/10/steven-seagal-biografia/ steven seagal biografia http://lavatrice-incassi-50.blogskine.net/node/produttore-lavatrice-industriale/ produttore lavatrice industriale http://party-50.mygreatblogs.net party http://doggy-stockings-80.mygreatblogs.net/blog/entry/ass-doggy-style/ ass doggy style http://mammifero-terrestri-90.mygreatblogs.net/motorizzazione-trasporto-terrestri/ motorizzazione trasporto terrestri http://brooke-shield-34.alumblogs.net/blog/entry/lana-brooke/ lana brooke http://trova-ascendente-99.alumblogs.net/2008/08/ritrovamento-marche-auricolare/ ritrovamento marche auricolare http://giucas-casella-79.alumblogs.net/2008/09/amante-e-casella/ amante e casella http://battaglione-lucetti-6.mygreatblogs.net/2008/07/30/battaglione-val-tagliamento/ battaglione val tagliamento http://sanpaolo-12.blogskine.net sanpaolo http://logistica-ortofrutta-70.mygreatblogs.net/logistica-it/ logistica it http://gregory-horror-43.mygreatblogs.net/gregory-colbert/ gregory colbert http://download-filemaker-29.alumblogs.net/2008/09/nod-download/ nod download http://congelatore-71.mygreatblogs.net/wordpress/piccolo-congelatore-orizzontale/ piccolo congelatore orizzontale http://boxing-gloves-47.alumblogs.net/node/foxy-boxing-gallery/ foxy boxing gallery http://anita-kelly-80.mygreatblogs.net/2008/08/25/scatti-anzianita-metalmeccanici/ scatti anzianita metalmeccanici http://roberta-palumbo-83.alumblogs.net roberta http://votazioni-sindaco-95.mygreatblogs.net/votazioni-comunale-verona/ votazioni comunale verona http://black-rhythm-82.blogskine.net/2008/09/cooler-master-centurion-black/ cooler master centurion black http://infermiera-lavoro-54.blogskine.net/lavoro-espansione-adiabatica/ lavoro espansione adiabatica http://cresto-renzo-50.alumblogs.net/2008/08/20/renzo-arbore-altogradimento/ renzo arbore altogradimento
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 28 sep 2008 10:11

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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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